The Postseason refers to games played after the end of the regular season to determine the league's champion. Between 1884 and 1890 postseason games were played only as exhibition matches. The first official World Series between the American League and the National League took place in 1903. There was no such postseason in 1904, however the tradition became permanent as of the 1905 season.
Up to 1968, the only postseason series was the World Series, featuring the teams that won their respective league pennants. The leagues were not yet divided into Divisions. The winners of the titles had to have the best overall record in their league. Those titles were sometimes decided by a one-game or three-game playoff, but these games were counted as part of the regular season.
With the expansion of 1969, the leagues were divided into Eastern and Western Divisions, necessitating League Championship Series, which became the first round of the postseason. From 1969 to 1984 these series were held as best-of-five playoffs, and from 1985 until 1993 they were best-of-seven playoffs. The two winners would then meet in the World Series, which became the second round of the postseason.
There was only one exception to this scenario, and it came in the 1981 Postseason. It was caused by the 1981 strike. The strike came in the middle of the season, so a decision was made after the strike was resolved to have the leading teams of each division from before the strike - the so-called "first-half champions" - play the leaders of each division from after the strike - the "second-half champions". See 1981 Split Season Schedule.
In 1994, the leagues were further divided into three divisions: Eastern, Central, and Western. In order for postseason play to produce a winner in an even number of match-ups, a Wild Card winner was chosen from each league. This would be the team from each league who had the best overall record among those that did not finish first in their division. The three division winners along with the Wild Card winner from each league played a five-game Division Series. Ironically, the first year of this new arrangement did not go as planned. The 1994 strike cut the season short and postseason play was cancelled for the first time in 90 years. The first such postseason scenario took place in the 1995 Postseason.
In 2012 the postseason was expanded again with the creation of a second wild card team in each league. This is the scenario that prevails today. The now two wild card teams per league play each other in a one-game winner-take-all round hosted by the team with the better record - the Wild Card Game. The winner then advances on to the Division Series to play the team with that league's best regular season record, regardless of division.
As a result there are now four rounds of postseason play:
- The Wild Card Game
- Best of 5 Division Series
- Best of 7 League Championship Series
- Best of 7 World Series
In February 2020, a proposal was floated in the New York Post to expand the postseason even further, by adding two wild card teams in each league, and giving a first-round bye to the team with the best overall record, which would go to directly to the Division Series. Then, the other two division winners would get a chance to pick the opponent they would host in a best-of-three wild card round, with the remaining two wild card teams playing the third wild card series. The three winners would advance to the next round and the rest of the postseason would then proceed as before. If accepted, the changes would be implemented in 2022, although initial reaction was mixed, with Trevor Bauer going on the record to say that Commissioner Rob Manfred must understand nothing about baseball to propose such a ridiculous plan.
Due to the coronavirus pandemic and the shortened regular season that resulted, the postseason was modified for the 2020 season only. Under this format, eight teams qualified for the postseason from each league: the first two teams in each of the three divisions, and the two teams with the next best records. These teams were then ranked 1 through 8, with team 1 playing team 8, in the first round and so forth. The Wild Card Game was scrapped, replaced by a preliminary round played entirely in the home ballparks of teams ranked 1 to 4 in a best-of-three format. The postseason then continued with the Division Series as usual.
- Mark Feinsand: "MLB considering new format for postseason", mlb.com, February 10, 2020. 
- Jerry Lansche: Glory Fades Away: The Nineteenth-Century World Series Rediscovered, Taylor Publishing, Dallas, TX, 1991. ISBN 0-87833-726-1
- Stuart Shapiro: "Measuring Franchise Success in the Postseason", The Baseball Research Journal, SABR, Volume 44, Number 2 (Fall 2015), pp. 32-36.