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In the first year of the cycle, every FIDE member nation would hold a national championship, with the top players qualifying for the Zonal tournament. The world was divided into distinct zones, with the USSR, United States and Canada each being designated a zone, thus qualifiers from these three zones went directly to the Interzonal. Smaller countries would be grouped into a zone with many countries. For example, all of South America and Central America combined originally formed one zone.
Players who won their Zonal tournaments, and who had scored above a prescribed level, typically received at least title norms towards international chess titles, such as International Master and Grandmaster; sometimes, winners could receive these titles outright, depending upon the strength of the zone.
The top players in each Zonal tournament would meet in the Interzonal tournament, which would typically have between 20 and 24 players. The top finishers (e.g., the top six in 1958) would qualify for the Candidates Tournament, which would take place the following year. They would be joined in the Candidates by the loser of the previous candidates' final and the loser of the previous world championship match. The winner of the Candidates tournament would play a 24-game match with the World Champion the following year, and need to win outright to gain the title.
To illustrate, the 1957 US Championship served as a Zonal tournament. The top three, Bobby Fischer, Samuel Reshevsky, and James Sherwin qualified for the Interzonal tournament that was held in Portorož in 1958. The top six at Portorož, (Mikhail Tal, Svetozar Gligorić, Tigran Petrosian, Pál Benkő, Friðrik Ólafsson and Fischer) qualified to the Candidates tournament. They were joined by Vasily Smyslov (loser of the 1958 rematch for the championship with Mikhail Botvinnik), and Paul Keres, who had finished second at the 1956 Amsterdam Candidates tournament. Those eight played a quadruple round-robin in the 1959 Candidates tournament. The winner was Tal, who then played Botvinnik a match for the championship in 1960.
Thus, Interzonal tournaments were held approximately every three years from 1948 until 1993. Their years of staging were in fact: 1948, 1952, 1955, 1958, 1962, 1964, 1967, 1970, 1973, 1976, 1979, 1982, 1985, 1987, 1990, and 1993. However, by 1972, the system was becoming unwieldy. The number of top-level players had grown, with the increasing popularization of chess, and the cost of staging these events had become too great. Also, new countries were joining FIDE, especially in Asia. From the 1970s, China, India, Indonesia and the Philippines started producing strong Grandmasters where there had been none before. Even Africa was demanding two zones. It had become impractical to put all of the top players into a round robin tournament, so in 1973 the system was changed to two Interzonals (with the first three in each qualifying for the Candidates). In 1982 it changed again to three Interzonal tournaments, where the top two players qualified from each. Further increases in the number of qualifiers led to the Interzonal being staged as a single Swiss system tournament in 1990 and 1993.
The system was dropped altogether from the mid-1990s, being replaced by a series of short, knockout-style matches among qualifiers.
See Candidates Tournament for a table of Interzonal, Candidates and World Championship results from 1948 to 2012.