The first type of precision-guided munition used in warfare, a guided bomb is an air-dropped bomb that adjusts its path to a target using aerodynamic control surfaces. Such bombs may be under human control or have autonomous guidance. They operate either on a go-onto-target or go-onto-location-in-space guidance model.
Many guided bomb designs later received a rocket booster, which formally makes them air-to-surface missiles rather than guided bombs, which are defined as unpowered. Guided bombs may have wings that let them glide for significant distances, especially when released at high altitude.
There were several attempts, of varying success, to use gliding bombs late in the Second World War, but the available sensing and guidance technology were inadequate for effective use. Even television cameras, a reliable commodity today, could only transmit a crude picture from the nose of a bomb.
The U.S. AZON was a conventional bomb that had been equipped with aerodynamic control surfaces, and could be steered, by radio from a human operator, left and right in azimuth, hence the name. An improved version, RAZON, could be adjusted in range (i.e., range and azimuth). Guidance and control were totally manual, based on what the weapon operator could see in the television link, and using switches to adjust fins to shift the name — it was not "flown" with a control stick as is an aircraft.
One of the problems of the AZON and related weapons is that to be guided, they could not roll, as did conventional bombs. Rolling, however, stabilized the flight path, so the weapons operator both had to correct drift and aim at the target.
While the German Fritz-X is often called a guided bomb, most models appear to have been was rocket-assisted and really an air-to-surface missile. It had dramatic results, sinking the Italian battleship Roma after Italy surrendered and Germany kept fighting.
First modern guided bombs
During the Vietnam War, the Paul Doumer Bridge was a critical and heavily-defended target, which had withstood hundreds of sorties with conventional bombs dropped by skilled crews, but had never been out of service for more than two months.
Rockwell International developed the GBU-8 laser-guided bomb (LGB) in 1967, but such weapons were not used against the Doumer Bridge until 1972. In comparison to the hundreds of aircraft sorties needed to deliver light damage, 16 F-4 Phantom II fighter-bombers struck the bridge in May 1972, using 2000 pound GBU-10 LGBs . This relatively small attack put the bridge, which carried four of the five railroad lines between North Vietnam and China, out of service for seven months.
Upgraded versions of the GBU-10 PAVEWAY bomb are still in service, although no longer the primary U.S. guided bomb. A laser-guided bomb can be extremely accurate, but requires good weather for visual observation, and a laser designator must be held on the target for the duration of the bomb's flight. While airborne designators have been developed that can continue to track the target, without human assistance, when dropped, the aircraft still has to remain in sight of the target and any of its air defenses. Laser designators and laser rangefinders, which use an invisible infrared beam, have been developed and are used by soldiers on the ground to control air support.
LGBs remain in service, but their technology is now reserved for niche applications, such as hitting moving targets. In service of the U.S. and many other nations, the guidance modes include inertial (often with GPS updating), radar, and electro-optical (most often infrared but sometimes visual light).
PAVEWAY laser guidance has gone through three U.S. generations, and PAVEWAY IV is in service with the Royal Air Force. PAVEWAY I LGBs were used late in the Vietnam War, followed by the improved PAVEWAY II, which had an improved laser seeker and "pop-out" fins. Both the I and II versions needed to be delivered from medium altitude. 
Developed to allow low-altitude delivery, PAVEWAY III, not immensely successful in its initial version, introduced an onboard computer autopilot to reduce operator workload. The computer also provided "proportional" control allowing the operator to use a joystick, rather than on-off switches, to "fly" the bomb on a much smoother path. 
PAVEWAY LGBs were the principal "smart" bombs used in the Gulf War. On the first night of Operation DESERT STORM, they were dropped, by F-117 stealth bombers, on targets in Baghdad. Their accuracy was such that for several hardened targets, one bomb blew a hole in a wall or roof, followed by another PAVEWAY sent through the hole and penetrating inside.
The GBU-28 was rapidly developed as a "bunker buster" weapon, but not derived from a conventional bomb. Instead, it used a guidance kit applied to a bored-out cannon barrel of immense strength. They were dropped from F-111 fighter-bombers. Even larger versions have been developed for the B-1, B-52, B-2, and F-15E Strike Eagle.
A more mundane application in DESERT STORM was "tank plinking", in which F-111 aircraft identified tanks, sometimes buried in sand, with their onboard thermal viewers, and then dropped a $10,000 PAVEWAY II on a $1,500,000 tank.  Other nations that make LGBs include Britain, France, Israel and Russia. A British-French cooperation produces the Matra BGL, although the Royal Air Force used PAVEWAYs in Middle East operations.
Electro-optical bombs go back to the Second World War, but became more practical in the 1960s. Today, they are niche weapons, typically for situations when the aircraft crew must do final target identification; these are "man-in-the-loop" weapons. A principal U.S. version is the GBU-15 and the air-to-surface missile derivative, the AGM-130.
Joint Direct Attack Munition
In U.S. inventory, the primary guided bomb is the Joint Direct Attack Munition (JDAM), whose basic Go-onto-location-in-space guidance is inertial, with the drop and target coordinates set by the aircraft just before drop. Newer versions use supplemental GPS guidance.
While troops on the ground can not directly control a JDAM, they can use a GPS-equipped laser rangefinder to take a precise sighting on the target and radio the data to the bomber. Still, the current JDAM can be used only against fixed targets; LGBs are still useful against moving targets when powered guided missiles are not appropriate.
The higher and faster that a basic guided bomb can be dropped, the farther the dropping aircraft can be from the target -- and safer from its defenses. This is one of the reasons that the attack version of the F-22 Raptor can drop from at least 50,000 feet and at supersonic speed, which gives it a much greater JDAM range than a current fighter-bomber or heavy bomber.
Even more range comes with the AGM-154 Joint Standoff Weapon (JSOW), known informally as the "flying pig". Where a JDAM is actually a guidance kit that bolts control fins to the tail of a conventional bomb, a JSOW deploys wings when launched, and can glide much farther than a JDAM.
The JSOW is used by the Air Force and Navy, but is a Navy program. 
Very large bombs
Go-onto-target guidance modes are in development to give guided bombs a capability against moving targets.
- Greg Goebel, [4.0 World War II Glide Bombs (2)]
- "Guided Bomb Unit-10 (GBU-10) Paveway II", Globalsecurity
- Greg Goebel, http://www.vectorsite.net/twbomb_05.html
- Carlo Kopp (Originally published July, 1992; Updated 2010), "DESERT STORM: Precision Guided Munitions", Air Power Australia
- Guided Bomb Unit-12 (GBU-12) Paveway II, Globalsecurity
- United States Navy, AGM-154 Joint Standoff Weapon (JSOW)