Aircraft carrier battles
While aircraft carriers have dominated naval warfare from World War II on, there have been surprisingly few aircraft carrier battles: engagements in which both sides had aircraft carriers, and indeed may not have seen one anothers' ships. By most accounts, there have been five such battles, as suggested in the title of a novel by naval historian Barrett Tillman, The Sixth Battle, about a hypothetical future battle. 
True carrier battles
- Battle of the Coral Sea (May 1942)
- Battle of Midway (June 1942)
- Battle of the Santa Cruz Islands (October 1942)
- Battle of the Eastern Solomons (August 1942)
- Battle of the Philippine Sea (June 1944)
Germany and Italy, in the Second World War, did not have operational aircraft carriers. British carriers in the early Pacific war were sunk by land-based aircraft, and, once the British carrier task force joined the Western Pacific forces, no Japanese carriers were left.
There are a great many operations, starting with the Battle of Taranto and the Battle of Pearl Harbor, and continuing through the Gulf War, in which carrier-based forces attacked land targets. A special case, the Battle of Cape Engano, involved attacks by U.S. carrier aircraft on Japanese carriers that had no aircraft.
During the Falklands War, Argentina had a carrier, but it never deployed operationally against the British force. Argentine Navy planes operated from land.
- Barrett Tillman (1992), The Sixth Battle, Bantam