He defeated female player Margaret Court in a match on Mother's Day 1973, the score 6-2. Court had achieved the Grand Slam in 1970, so was at her peak.
Navatilova lost 7-5, 6-2, even though she was allowed two serves to Conner's one and played to the doubles court.
During the 1998 Australian Open, sisters Serena and Venus Williams boasted that they could beat any man ranked outside the world's top 200.
Neer was the eighth ranked American male player at the time, and Moody was the reining Wimbledon chamopion.
Probably the most famous tennis battle of the sexes took place in 1973, between Bobby Riggs, winner of the Wimbledon men's singles title in 1939, who was aged 55 and still playing some tennis in 1973 but was well past his prime.
There is a long history of female tennis players thinking they can compete with the men, and finding out that it is not as easy as they think.