He achieved his career-high doubles ranking of world No. 7 in August 2019, and has won 19 doubles titles on the ATP Tour, including two at Masters 1000 level. Klaasen is a two-time Grand Slam finalist, having finished runner-up at the 2014 Australian Open alongside Eric Butorac, and the 2018 Wimbledon Championships with Michael Venus. He was also runner up at the ATP Finals in both 2016 and 2019, partnering Rajeev Ram and Venus respectively.
In singles, Klaasen has a career-high ranking of world No. 208, achieved in October 2011.
He has represented South Africa in the Davis Cup since 2009, and has a win–loss record of 13–4.
(W) winner; (F) finalist; (SF) semifinalist; (QF) quarterfinalist; (#R) rounds 4, 3, 2, 1; (RR) round-robin stage; (Q#) qualification round; (P#) preliminary round; (DNQ) did not qualify; (A) absent; (Z#) Davis/Fed Cup Zonal Group (with number indication) or (PO) play-off; (G) gold, (S) silver or (B) bronze Olympic/Paralympic medal; (NMS) not a Masters tournament; (NTI) not a Tier I tournament; (P) postponed; (NH) not held; (SR) strike rate (events won / competed); (W–L) win–loss record.
To avoid confusion and double counting, these charts are updated at the conclusion of a tournament or when the player's participation has ended.