Third Indochina War
After the Fall of South Vietnam in 1975, peace did not come to Vietnam, but series of conflicts directly involving Vietnam, Cambodia, and China began to flare in 1978, which waxed and waned until a treaty in 1991, with small-scale actions until 1999. It was preceded by conflicts with Cambodian groups before the South fell, and increasing tensions with China.
France, and then the U.S., had claimed a "special relationship" with Vietnam, but Vietnam claimed a "special relationship" with Laos and Cambodia. Essentially, Vietnam expected them to treat it as the senior state and follow its guidance. In turn, China believed it had a special relationship as well, in which both Vietnam would generally support Chinese policy, and, in particular, Chinese Communism against Soviet Communism.
The Vietnamese, however, had good reason to feel secure in their military power, if they ignored the political context. The People's Army of Viet Nam captured much of the equipment of the ARVN, and was now among the most experienced armies in the world. While its operations in 1975 did not show mastery of high-technology combined arms warfare, it became a very credible opponent, in direct combat, for forces lower in technology than the Warsaw Pact or NATO. While many of the personnel of the ARVN were purged or imprisoned, others eventually joined the new forces, bringing their expertise.
The PAVN had been growing for 40 years, and indeed reached its greatest size in 1976. PAVN infantry divisions were increased from 27 to 61 (48 regular infantry divisions and 13 smaller economic construction divisions), and military corps from six to 14. The Vietnamese Air Force was raised from three to five Air Divisions including one helicopter division. The Vietnamese Navy doubled the number of its combat vessels. 
According to Pike, in late 1990 about 500,000 had been demobilized from the PAVN (apparently to about 800,000 regulars and 1.6 million militia). Vietnam had to cope with huge destruction in both North and South, not only repairable damage to buildings and infrastructure, but much more difficult problems with unexploded ordnance and chemical contamination. 
Aside from the specialized tasks, the Vietnamese government did not have extensive experience with economic recovery. Their model was a centralized Stalinist one, which they themselves rejected with the introduction of doi moi Vietnamese-style markets, but not until 1986.
Expectations of aid
As part of the Paris Peace Talks, there had been a 1973 agreement for aid to Vietnam, but Congress refused to fund it with language in in Public Law 94-41, a continuing appropriations resolution signed by President Gerald Ford in the summer of 1975.  A large part of the refusal centered on the issue, extremely sensitive in the U.S., of the fate of American military personnel held prisoners of war (POW), as well as those missing in action (MIA) in Vietnam. The first official U.S. mission to Vietnam, in 1977, was led by Leonard Woodcock, former head of the United Auto Workers and a representative of Jimmy Carter; his mandate was first to address the POW-MIA situation, and then explore aid; the Vietnamese were optimistic. In February 1977, "So certain of developing these ties were the Vietnamese that a group of oil executives visiting from Japan had been told in late 1976 that future development of Vietnam’s substantial petroleum interests “was reserved ‘for the American sector.’” “Washington, in turn, seems almost ready to accept the fact that the fate of most of the MIAs will never be known.”
Prior to the Woodcock mission, there had been an unpublicized three-week trip by representatives of the World Bank and two separate missions by the United Nations Development Programme [UNDP]. Normalization of relations with the U.S. was seen as key; the UNDP told the Vietnamese that they alone could not fund the projects under discussions, additional donors would be needed, and the "Vietnamese know who the donors could be."
While there is now considerable cooperation between Vietnam and the United States, the situation was tense immediately after the war. Young suggests that a normalization between Vietnam and the United States, sought in 1977, might have reduced tension. 
Several factors contributed to making normalization more difficult. The POW-MIA issue was extremely sensitive politically. Further, power, in the Carter Administration shifted between the U.S. Secretary of State, Cyrus Vance, and the National Security Adviser, Zbigniew Brzezinski.
Vance's plans were broader, and included normalization with both China and Vietnam, a new arms control agreement with the Soviets, and a continued warming of the Cold War. Brzezinski's thinking was focused on the Soviets, and judged actions in how they could be used to pressure the Soviets. He sought a tilt to China as a pressure on the Soviet Union, and, if that annoyed the Vietnamese, whom he saw as Soviet puppets, it was fine with him. According to his aide Michel Oksenberg, Brzezinski despised the Vietnamese and called the "cesspool of civilization". Carter wrote in his diary that "He was overwhelmed with the Chinese. I told him he had been seduced."
Richard Holbrooke had met with Vietnamese Foreign Minister Nguyen Co Thach at the Vietnamese mission to the United Nations, and, while they agreed in principle, Brzezinski continued to object. At the end of October 1978, normalization depended on conditions unacceptable to the Vietnamese, which, within months, were made moot by the Chinese invasion:
- Calming of hostilities between Vietnam and Cambodia
- Loosening of the alliance between the Soviets and Vietnamese
- Stopping Chinese emigration from Vietnam. 
Vietnam invades Cambodia
Vietnam announced, on 2 December, the formation of the “Kampuchea National United Front for National Salvation,” working to remove the Pol Pot regime from power. By the time U.S.-China normalization was announced on the 15th two Vietnamese divisions were in Cambodia; an eleven-division PAVN force moved in, on December 25, 1978.
Phnom Penh, the Cambodian capital fell on January 7, leading to ten years of Vietnamese occupation, and almost 13 years of civil war.  On January 14, however, Thai, Chinese, and Khmer Rouge leaders formed a guerrilla alliance to fight the Vietnamese. In Douglas Pike's opinion, the Politburo, now more accustomed to success through conventional arms, not even armed dau trinh, believed they could quickly use their military against Cambodia and get a quick result. 
Normalization between the U.S. and China was announced on December 15, and Deng Xiaoping arrived in Washington a month later. Brzezinski gained Carter's support in getting U.S. agreement to China's planned punitive response into Vietnam.  Given the Vietnamese invaded with relatively high technology, were frustrated by guerrillas who had sanctuaries into which they could retreat, and that it seemed an endless war, cynics have called it "Vietnam's Vietnam". The action was "deplored" by the Association of Southeast Asian Nations, (ASEAN)  with a statement from the then-chairman of the ASEAN Standing Committee, Indonesian Minister of Foreign Affairs Mochtar Kusumaatmadja; this became the ASEAN position. ASEAN members brought the matter to the United Nations Security Council.
China invades Vietnam, 1979
In response to the Vietnese invasion of their client, Cambodia, China invaded Vietnam in February 1979. Young states that this was with the foreknowledge and approval of the United States. The Chinese People's Liberation Army sent 180,000 troops in a five-pronged attack against an estimated 75,000 to 100,000 PAVN regular and border troops, using essentially the same tactics as they had used in the Korean War. The PLA achieved tactical surprise, but did not use its manpower advantage, trade space for time, or use deception techniques. Ironically, the attack took place in areas that the U.S. avoided during the Vietnam War, over concern of triggering Chinese intervention.
In general, the PAVN equipment, including that captured from the ARVN, was more advanced than the Chinese, especially with respect to communications. Neither side used close air support. but the PAVN did resupply its units by parachute drop. There appeared to be no Chinese equivalent to the elite PAVN sappers., The Chinese eventually seized three provincial capitals, Lao Cai City (the capital of Lao Cai Province is now Dien Bien Phu), Cao Bang and Lang Son, and withdrew a month later.  after losing nearly half as many soldiers killed in action in Vietnam as the U.S. had lost in 10 years. 
Chinese commanders in this war were to achieve later political prominence. Zhang Wannian commanded the 127th Division (which was transferred to the 54th Army as its parents 43rd Army and Wuhan MR were eliminated in the 1985 downsizing). Fu Quanyou commanded the 1st Army in the battle to take Mount Laoshan in 1984 during the protracted post-1979 Sino-Vietnamese border skirmishes. Both men later jointed the Central Military Committee of the Party.
Cambodia after the Chinese invasion
In September of 1979, the UN took up the question of seating the Vietnamese-backed Cambodian PRK government under Heng Samrin, over Pol Pot's Khmer Rouge. This gave the U.S. four unpleasant choices following the bad publicity of the Chinese invasion following normalization: available: it could vote in favor of the Vietnamese-led PRK, which would certainly anger the it could vote to seat the Khmer Rouge, which would demonstrate support for the China/ASEAN position
- Back the PRK allies of the Vietnamese, and accept the view of the country to which it had been hostile for several years, angering China and the ASEAN nations, all of which had been vocal in their opposition to the Vietnamese occupation;
- Choose the Khmer Rouge, the group that over a year earlier President Carter labeled
“the worst violator of human rights in the world today.
- Vote not to seat any Cambodian delegation until the war was resolved, leave the seat empty until such time as the situation in Cambodia was resolved, which would implicitly accept the Vietnamese occupation and leaving the Cambodian people without representation;
- abstain from the vote, irritating China and ASEAN, but have been consistent with a position of neutrality.
The U.S. chose to vote to seat the Khmer Rouge.
1983 Vietnam-China fighting
In the autumn of 1983, the 95th PAVN regiment conducted what were termed 'training exercises' in Cambodia. On March 24, 1984, other PAVN units attacked Khmer Rouge headquarters, while the 95th Regiment crossed into Thailand to block the Khmer Rouge retreat. China responded with heavy shelling of towns on the Sino-Vietnamese border.  The PAVN withdrew from Thailand in early April, but the shelling continued, and the PAVN units in Cambodia continued until they overran the Khmer Rouge headquarters on April 15.
The Chinese then attacked toward the Laoshan hills on the border, fighting from May to July. In yet another irony, the Chinese headquarters was in Kunming, where the Viet Minh had met with the U.S. Office of Strategic Services team during the Second World War. The Laoshan area is considerably farther from Hanoi than was the 1979 attack, and the reasons for picking this site are not known. O'Dowd speculated that one reason may have been to draw PAVN troops out of Cambodia, just as the Battle of Khe Sanh may have been meant to draw U.S. troops away from the cities to be attacked in the Tet Offensive. China may also have wanted the psychological victory of capturing a provincial capital that could not easily be reinforced, Ha Giang City. The Chinese failed to take Ha Giang, and were beaten to a stalemate much as in 1979. 
As an example of the conflict, Peking Daily made the claim in a story about a local war hero identified as Xu Xiaodan, a scout for artillery units near Laoshan, a frequently reported flashpoint in the six-year-old undeclared China-Vietnam border war. No exact date or Chinese casualties were given in the Associated Press report from 1985 report, which followed two days after a Vietnamese report forces killed 313 Chinese soldiers last month in repulsing "land-grabbing attacks" in its Ha Tuyen Province, which borders the Yunnan province of China. Smaller-scale artillery exchanges and border incidents between China and Vietnam ended in November 1991. <
A 1988 estimate put the PAVN at 1.2 million in the regular "main force" and 1.7 million in the militia or "para-military" force). A demobilization program planned to send 800,000 back to civilian life, still leaving a military establishment with 1.6 million personnel. Probably in June 1988, the Vietnamese decided to accept their losses and, with great ceremony, start withdrawing ground troops to let the Cambodians fight their own civil war.
Cambodian settlement of 1991
In this situation, Thailand, an ASEAN member, was the "frontline state". ASEAN faced a problem of showing support for Thailand but Indonesia decided that the apparent strategy of prolonging the war and "bleeding Vietnam white", was not in the interest of Southeast Asia as a whole. It was believed that Thailand was providing sanctuary to the Khmer Rouge, frustrating the Vietnamese generals who were forbidden to pursue into Thailand, much as the Americans were not allowed to pursue the Viet Cong into Laos and Cambodia.  While always insisting on the central demand of Vietnamese withdrawal and Khmer self-determination, Indonesia encouraged the Khmers and Vietnamese and their external sponsors to a more stable settlement. Negotiations for such a settlement began in 1982, and ended with the Final Act of the Paris International Conference on Cambodia on October 23, 1991. Mochtar and the next Indonesian foreign minister, were key in these negotiations.
These accords mandated elections and a ceasefire, which was not fully respected by the Khmer Rouge, and UN-sponsored elections in 1993 helped restore some semblance of normalcy under a coalition government. Factional fighting in 1997 ended the first coalition government, but a second round of national elections in 1998 led to the formation of another coalition government and renewed political stability. The remaining elements of the Khmer Rouge surrendered in early 1999. 
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