|Before the official World Champions|
|Giaochino Greco||1620-34 Italy|
Chess existed a long while before Greco came along, but he was pretty clearly the best chess player of his time and worth knowing about.
There were all sorts of players after that who might have been the best in the world, like Philidor, Saint-Amant, and Staunton.
We pick up the story a long while later, with some players who equally clearly were the best of their time:
|Adolf Anderssen||1851–58,1862–66 Prussia|
|Paul Morphy||1858–62 United States|
Morphy stopped playing chess in 1859. After Anderssen won the first international all-play-all tournament in London, 1862, he was once again seen as the best active player in the world.
In 1886, Wilhelm Steinitz beat Johannes Zukertort in a match which was agreed to be for the title of World Chess Champion. Steinitz had previously beaten Anderssen in a match in 1866, so he may have been the best in the world since then, although that wasn't generally accepted until the 1870s.
|Wilhelm Steinitz||1886–94 Austria-Hungary, USA|
|(Hastings 1895:||a strong tournament)|
|Emanuel Lasker||1894–1921 Germany|
|(Carl Schlechter of Austria-Hungary drew a match with Lasker)||1910|
|José Raúl Capablanca||1921–27 Cuba|
|Max Euwe||1935–37 Netherlands|
* Died while still champion. Botvinnik won a 5-player four-round all-play-all tournament organised in 1948, playing Smyslov, Reshevsky, Euwe, and Keres.
|Mikhail Botvinnik||1948–57, 58–60, 61–63 Soviet Union (Russia)|
|(David Bronstein of the USSR drew a match with Botvinnik)||1951|
|Vasily Smyslov||1957–58 Soviet Union (Russia) (Drew match in 1954)|
|Mikhail Tal||1960–61 Soviet Union (Latvia)|
|Tigran Petrosian||1963–69 Soviet Union (Armenia)|
|Boris Spassky||1969–72 Soviet Union (Russia)|
|Robert Fischer||1972–75 United States|
|Anatoly Karpov||1975–85 Soviet Union (Russia) (and drew in 1987)|
|Garry Kasparov||1985–93**,1993–2000 Soviet Union (Russia)|
|** In 1993, the World Champion, Garry Kasparov, decided to organise his own match, and so did FIDE, and so there were two World Champions from 1993-2006, but Kasparov was definitely the best player until 2000, and Kramnik, who beat him, later beat Topalov, who was then the FIDE Champion, in a unification match in 2006.|
|Vladimir Kramnik||2000–07 Russia|
|(Peter Leko of Hungary drew a match)||2004|
|Viswanathan Anand||2007–13 India|
|Magnus Carlsen||2013–present Norway|
|Not World Champions|
|Xavery Tartakower||Poland, Austria, France (The world champion of chess writing)|
|Judit Polgar||Hungary (The best female player ever)|