His career began as an amateur and Riessen won numerous tournaments as such, as in Cincinnati. With the start of the Open Era Riessen was professional.
Riessen was especially active in the double, where he was able to win a total of 52 items. Most of the titles he won it on the side of the Dutchman Tom Okker, but also with his fellow countryman Sherwood Stewart, he formed a successful team. With Okker Riessen attracted a total of four times in a Grand Slam final, but they could win the game only at the U.S. Open in 1976. This was his second Grand Slam title, having won in 1971 at the French Open together with Arthur Ashe the tournament. With Stewart, he was also still in 1978 at the U.S. Open in the finals, but they lost Robert Maud and Ken Rosewall. His best finish in the world rankings, he reached third place on 3 March 1980 In Single Riessen celebrated several successes. Except at the French Open he reached in all Grand Slams the quarterfinals. During his career he won a total of six tournaments for themselves. On September 4, 1974, he was listed in eleventh place in the world rankings in singles, his best finish.
In the mixed doubles Riessen moved nine times in a finale, of which eight times with Margaret Smith Court The duo won six of the eight common Finals, including any Grand Slam tournament. Thus, they completed even as their team career Grand Slam in mixed doubles. With Wendy Turnbull Riessen won his seventh mixed title at the U.S. Open in 1980.
Between 1963 and 1981, Riessen played eight games for the U.S. Davis Cup team. He won it three out of four single and four double six games. Both in his first season as well as in his final season with the team Riessen won the Davis Cup, even though he was not employed in the finals.