International competitors include reigning world champion Carlsen Magnus of Norway and home favourite Jan-Krzysztof Duda.
Magnus Carlsen. Photo: PAP/Leszek Szymański
The event at Warsaw's National Stadium runs until Thursday.
Coronavirus restrictions foiled the world chess body FIDE's original plan to hold the championships in Nur Sultan, Kazakhstan.
Polish Prime Minister Mateusz Morawiecki said: "The game of chess is an important part of the history of Poland. I am very glad to know that our country will host the best grandmasters for the World Blitz and Rapid Chess Championships."
The 2021 World Rapid and Blitz Championships have a total prize fund of USD 1 million, with a top prize of USD 60,000 each going to the rapid and blitz open champions and USD 40,000 each to the women's champions.
Earlier this month, more than 550 chess players from 21 countries took part in the 2021 European Blitz and Rapid Chess Championships, which were held in the southern Polish city of Katowice.
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Source: europechess.org