The closest they came was reaching the final on two occasions, first losing to Italy in 1938, and then to West Germany in in 1954.
They had beaten the Germans 8-3 in the group stages of the tournament and were expected to walk the final, but somehow conspired to lose 2-1 when it mattered most.
They have produced legends of the game like Ferenc Puskás, József Bozsik and Flórián Albert, but it is two lesser-known stars who hold FIFA World Cup records.
The first is Sándor Kocsis, a prolific striker who scored an incredible 75 goals in just 68 games for his country between 1948 and 1956. He is written into FIFA World Cup history when he finished top-scorer at the 1954 tournament in Switzerland and in doing so claimed a number of records.
He was the first player to score two hat-tricks at the finals, through that has since been matched by Just Fontaine (France, 1958), Gerd Müller (West Germany, 1970), and Gabriel Batistuta (Argentina, 1994 and 1998). He also jointly holds the record for the most games in a row in which he scored two goals (four).
Kocsis died at the age of 49 in what many say was a suicide as he fell to his death after hearing that he was terminally ill with cancer.
The second Hungarian to appear in the World Cup record books is László Kiss, who has the record for the fastest-ever hat-trick in FIFA World Cup history.
He netted three goals in eight minutes after coming off the bench against El Salvador in the 1982 tournament in Spain. He is also the only substitute to ever net a hat-trick. Hungary won the game 10-1.