Kotyza started coaching Petra Kvitová in November 2008; by this time, Kvitová had entered the World's Top 50 and had already reached the round of 16 of the 2008 French Open in what was her first appearance in the main draw of a Grand Slam tournament.
Under Kotyza, Kvitová continued to make gradual progress on the WTA Tour and in May 2011 she reached the world's top ten for the first time, by virtue of winning the Mutua Madrid Open. This was followed by a breakthrough first Grand Slam title at Wimbledon, where she defeated Maria Sharapova in the final to become the first Czech player since Jana Novotná to win a title at this level, and the prestigious 2011 WTA Tour Championships at the end of the season. In twelve months, Kvitová had gone from World No. 34 at the end of 2010 to achieving a career high rank of No. 2 at the end of 2011.
Kotyza was also a head coach of the Czech Republic Fed Cup team but stepped down in 2012 to focus on coaching Kvitová. In January 2016, Kotyza and Kvitová parted ways. Kotyza coached Caroline Wozniacki from April to August 2016. From December 2016 to September 2017 he coached Karolína Plíšková. They split after 2017 US Open.
- Petra Kvitova flashes firepower on court, shy smiles off it USATODAY
- iDNES.cz: Muž ve stínu má jednoduchý život. Nechci udusit hvězdu, říká trenér Kvitové, M. Kučerová, 27.10.2011
- Jan Kodes: Watch out for Petra Kvitova World Tennis Magazine
- Petra Kvitova tops Maria Sharapova at Wimbledon for first Grand Slam title, Washington Post
- Kvitova wins WTA Championships, Al Jazeera English
- Kvitova beats Errani to capture Dubai title, ABC News (Australian Broadcasting Corporation)
- "Petra Kvitova fires coach David Kotyza after 7 years". Sports Illustrated. 25 January 2016. Retrieved 1 February 2016.