Inducted into the Australian Tennis Hall of Fame in August 1996; inducted into the International Tennis Hall of Fame in 1991; inducted into the Sport Australia Hall of Fame in 1987.
Ashley Cooper was an attacking player with smooth groundstrokes and poise at the net. In 1958 he came close to completing the Grand Slam, but fell in the semifinals at the French Open. He is one of only nine men to win three majors in a season.
He won back-to-back Australian Open titles in 1957 and 1958, and featured in Australia's Davis Cup team in both years. In 1957 the Australians triumphed over the United States 3-2, but in 1958 the result was reversed, with the Americans defeating the Australians 3-2.
In the Queen's Birthday Honours List of 2007, he was appointed an Officer of the Order of Australia (AO) for his service to tennis.