In the second half of the 1960s and the first half of the 1970s, Davidson was considered one of the world's best doubles and mixed players. Together with his playing partners, he managed to win ten tournaments in doubles. Two of them were the titles in the major Grand Slam competitions of the Australian Championships (today's Australian Open ) and US Championships (today's US Open ) in 1972 and 1973 . In addition, Davidson reached four Grand Slam finals, but they were lost. In total, his ten double victories are compared to 13 winless finals.
His mixed career was much more successful. In total, he won eleven titles in twelve Grand Slam finals within nine years. 1967 - Davidson was one of the few players alongside Lewis Hoad and Luis Ayala to be independent while most of the others had contractual ties - he achieved the rare feat of a Grand Slam by winning all four of the relevant tournaments that year. However, he did not always succeed in doing this with the same partner. At the Australian Championships at the beginning of the year he still played alongside Lesley Turner , while Billie Jean King always accompanied him in the remaining three Grand Slam tournaments of the year and the five victorious appearances at Grand Slam tournaments in the following years .
Davidson was also active in the individual competition. Here he has a negative career record, but in the pre-open era, i.e. the years up to and including 1967, he managed to reach eight quarter-finals and one semi-finals in Grand Slam tournaments within six years. In the latter he moved to the Wimbledon Championships in 1966.
Davidson was the athletes' official spokesman several times at the Wimbledon Championships. From 1971 to 1980 he was director of the John Newcombe Tennis Ranch in New Braunfels, Texas . What is remarkable about Davidson is the fact that he already worked as a coach during his playing career. From 1967 to 1970 he looked after the British team in the Davis Cup . From 1974 Davidson played in the US league World TeamTennis . There he joined in 1974 with Bob Hewitt for the Minnesota Buckskins . He then moved to the Hawaii Leis and had John Newcombe in 1975 and Ken Rosewall in 1976 and Ilie Năstase as playing partners. He quickly became a crowd favorite in this league. In particular, the games with his good friend Newcombe enjoyed great popularity and the audience cheered the great camaraderie of the two compatriots and was amused by their matching mustaches. In 1982 Davidson was coached by the Houston Astro-Knots in World TeamTennis and returned briefly four years later as a player and coach of the Boston Bays .
His final resignation from active professional sport he announced in 1991. In July 2009, the Giammalva Racquet Club in the Texan town of Spring near Houston hired him as one of its trainers. A few months later, in September, Davidson was nominated for induction into the International Tennis Hall of Fame . He received this honor the following year.