The Kasparov-Short match was held under the sponsorship of the PCA, and FIDE was left with a sham match between two players whom Short had already defeated. Kasparov won the match convincingly and defended his title against Viswanathan Anand of India in 1995. The primary sponsor of the PCA was Intel — but after the 1995 match, Intel withdrew its support, and the PCA was history.
Negotiations for a reunification match between players with a claim to being champion continued to flounder. A non-FIDE-sanctioned match between Kasparov and Vladimir Kramnik of Russia in 2000 ended in Kasparov's defeat. Although most people still considered Kasparov the world's best player, he was thwarted in his attempts for a rematch.
These goings-on call into question a fundamental historical division in chess: Does the title of world champion belong to the titleholder, or to the organization that grants it?
For a few years the chess world lived with the bizarre notion of two world champions. Most serious players considered Kramnik the actual champion during this time, but FIDE organized what it termed "official" championships won by different players. Finally, a reunification match was held in 2006 in which Kramnik defeated Bulgaria's Veselin Topalov to seemingly settle this issue.
FIDE further muddied the waters by introducing a world championship tournament, which supposedly replaced the more traditional match format. In 2007, Viswanathan Anand won the tournament to become the "official" champion.
Thankfully, in 2008, Kramnik and Anand played a match won by Anand. Anand defended the title in 2010 against Topalov, and was then considered the undisputed champion. Order had been restored. In 2013, Norway's Magnus Carlsen defeated Anand to become world champion. He beat Anand again in 2014 to successfully defend his title.