Alexander Alexandrovich Alekhine, Ph. D. (October 31 [O.S. October 19] 1892 – March 24, 1946) (Russian: Алекса́ндр Алекса́ндрович Але́хин, pronounced [ɐlʲɪkˈsandr ɐlʲɪkˈsandrəvʲɪtɕ ɐˈlʲexʲɪn]) was the fourth World Chess Champion. He is often considered one of the greatest chess players ever.

By the age of twenty-two, he was already among the strongest chess players in the world. During the 1920s, he won most of the tournaments in which he played. In 1927, he became the fourth World Chess Champion by defeating Capablanca, widely considered invincible, in what would stand as the longest chess championship match held until 1985.

In the early 1930s, Alekhine dominated tournament play and won two top-class tournaments by large margins. He also played first board for France in five Chess Olympiads, winning individual prizes in each (four medals and a brilliancy prize). Alekhine offered Capablanca a rematch on the same demanding terms that Capablanca had set for him, and negotiations dragged on for years without making much progress. Meanwhile, Alekhine defended his title with ease against Bogoljubov in 1929 and 1934. He was defeated by Euwe in 1935, but regained his crown in the 1937 rematch. His tournament record, however, remained uneven, and rising young stars like Keres, Fine, and Botvinnik threatened his title. Negotiations for a title match with Keres or Botvinnik were halted by the outbreak of World War II in Europe in 1939. Negotiations with Botvinnik for a world title match were proceeding in 1946 when Alekhine died in Portugal, in unclear circumstances.

Emanuel Lasker (December 24, 1868 – January 11, 1941) was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years. In his prime Lasker was one of the most dominant champions, and he is still generally regarded as one of the strongest players ever.

His contemporaries used to say that Lasker used a "psychological" approach to the game, and even that he sometimes deliberately played inferior moves to confuse opponents. Recent analysis, however, indicates that he was ahead of his time and used a more flexible approach than his contemporaries, which mystified many of them. Lasker knew the openings well but disagreed with many contemporary analyses. He published chess magazines and five chess books, but later players and commentators found it difficult to draw lessons from his methods.

Lasker made contributions to the development of other games. He was a first-class contract bridge player and wrote about bridge and other games, including Go and his own invention, Lasca. His books about games presented a problem which is still considered notable in the mathematical analysis of card games. Lasker was also a research mathematician who was known for his contributions to commutative algebra, which included proving the primary decomposition of the ideals of polynomial rings. On the other hand, his philosophical works and a drama that he co-authored received little attention.