After Alekhine lost his title in the match against Euwe in 1935, he got in shape and was much more serious and in much better sportive form for the rematch in 1937.
Alekhine - Euwe - 1937
Euwe was a mathematician, 5th world champion, and the only one from the Netherlands (at least until now). He was also president of FIDE from 1970-1978. Some sources say that the “issues” with Fischer could be resolved thanks to him, which means that the most well-known world championship match could be played. (1972 - Fischer vs. Spassky). So, several GMs usually say that Euwe was an outstanding FIDE president.
Max Euwe in 1973
As a player, he was unquestionably strong, but in the rematch, he simply had no chance: Alekhine was such a strong, imaginative, and powerful player, and when he was at his best, he would merely crush his opposition. The rematch was played again in the Netherlands, in 7 cities this time, and Alekhine won convincingly 10-4, with 11 draws.
Then comes 1938, and the famous AVRO tournament of 8. Keres won ahead of Fine, and Botvinnik was 3rd. After the event, both Botvinnik and Keres challenged Alekhine for the world title match. They negotiated, but we know what happened from 1939-1945. Alekhine played in the famous Olympiad in Buenos Aires in 1939 for France on board 1. He got a silver medal on board 1, and Capablanca won the gold medal on board 1! They even started to negotiate again for a world title match, but the war stopped everything.
Alekhine was one of the few players who returned from Argentina to Europe.
After the war, negotiations with Botvinnik were renewed. But then, Alekhine suddenly died, which makes him the only player who passed away as world champion!
After that, a tournament was organized in 1948 by FIDE to determine the new world champion. It meant the end of an era where top players could challenge the world champion directly and negotiate with him about the match. FIDE took over.
FIDE wanted to recreate the AVRO tournament, but Alekhine and Capablanca died in the meantime. FIDE organized a tournament of 6 players who would play in a quadruple round-robin tournament. Flohr was replaced by Smyslov, and Fine decided to renounce, leaving the lot with only 5 players!
Eventually, a tournament for the world title was played in 1948, with 5 players playing a quintuple round-robin (5 games against each opponent). The tournament was played in the Netherlands and USSR.
Botvinnik won, and his era began. He lost his title and managed to get it back 2 times (vs. Tal and Smyslov)! Finally, he lost his title vs. the famous Armenian GM Petrosian in 1963. This means that Botvinnik was champion for almost 15 years. Not so bad!