The Major League Baseball postseason is an elimination tournament held after the conclusion of the MLB regular season. As of 2012, the playoffs for each league--American and National--consist of a one-game wild-card playoff between two wild card teams, two best-of-five Division Series (LDS) featuring the wild-card winner and the winner of each division, and finally the best-of-seven League Championship Series (LCS). The winners of the American League Championship Series (ALCS) and the National League Championship Series (NLCS) play each other in the best-of-seven World Series.
Major League Baseball is the oldest of America's major professional sports organizations, with roots dating back to the 1870s. As such, it is steeped in tradition. The final series to determine its champion has been called the "World Series" (originally "World's Championship Series" and then "World's Series") as far back as the National League's contests with the American Association starting at the beginning of the 1880s.
In 1903, the two modern Major League Baseball leagues began annual postseason play with a one-round system in which the American League team with the best record faced the National League team with the best record in a best-of-seven series (in 1903, 1919, 1920, and 1921 it was best-of-nine) called the World Series; however, there was no 1904 Series because the National League Champion, the New York Giants, refused to play. This single-tiered approach persisted through 1968, even with the expansions of 1961-1962 that expanded both leagues to 10 teams.
In 1969, both leagues expanded to twelve teams, which made it more difficult to compete for a league championship because there were more teams competing for the AL and NL pennants. In addition, a team would play other clubs in its own region of the country more than clubs in the rest of the country, creating an unbalanced schedule that in some years could give a team from one region an advantage in fighting for a single pennant. To remedy this, and imitating the other major sports' long-standing playoff traditions, Major League Baseball split each league into Eastern and Western divisions, creating four divisions overall and no worse than a sixth-place finish for any team in any division until later expansions in 1977 and 1993. This created a new postseason round, which was dubbed the League Championship Series (LCS), a best-of-five series. In 1985 the LCS was expanded to a best-of-seven series.
Under this system, it was possible for one of the best teams in a league to be left out of the postseason if it didn't win its division. Most notably, in 1993, the Atlanta Braves and San Francisco Giants finished with the two best records in the majors, with 104 and 103 wins, respectively. However, since both teams played in the National League West, the Giants missed the postseason by a single game.
The baseball players' strike of 1981 uniquely--for this era--added another round to the postseason. Because the strike split the season into two roughly equal halves, the division winners of each half of the 1981 season first met in a best-of-five Division Series. The winners of the division series then progressed to the league championship series, with the remainder of the postseason following a similar format to other years in this era.
Major League Baseball went through a realignment in 1994, when both the American and National leagues expanded to three divisions: Eastern, Central, and Western. To avoid a playoff with an odd number of divisional winners, the league added a wild card playoff spot to each league, imitating the original post-merger NFL system. The wild-card for each league would be the team with the best record which did not win their division, eliminating a circumstance where a team with the second-best record in the entire league would miss the playoff because of not winning its division. This new format doubled the postseason contenders in each league from two to four, and from four teams overall to eight. The addition of a second wild card spot would come in 2012.
The additional teams meant another elimination round was necessary. This new round would become the new first round of the postseason, the best-of-five Division Series. This term had first been used for the extra round required in 1981 due to the "split-season" scheduling anomaly following the midseason baseball players strike. This format was in place for the 1994 season, but that year's players' strike canceled the postseason. The format was realized on the field in 1995.
Under this format, in the two Divisional Series, the wild card team played the divisional champion outside its own division that had the better record, with the remaining two teams playing each other in the second Division Series for each league. The two Division Series winners from each league go on to play each other in the League Championship Series. As with the previous postseason format, the winners of each League Championship Series met in the World Series.
With the adoption of the new collective bargaining agreement in November 2011, baseball commissioner Bud Selig announced that a new playoff system would begin within two years; the change was ultimately put into place in 2012. The format chosen was the one-game Wild-card playoff.
Under this format, a second wild card team has been added to each league, i.e., the team with the second-highest win total in each league among non-division winners. The two wild card teams play in a one-game playoff after the end of the regular season, with the winner advancing to the Division Series. The divisional champions qualify for the Division Series just as in the previous format; however, under the expanded wild card format the winner of the one-game wild card playoff faces the top-seeded divisional champion in the Division Series, regardless of whether the two teams are in the same division, while the second- and third-seeded divisional champions play each other in the other Division Series. The format for placement in the League Championship Series and World Series remains.
The World Series used several different formats in its early years. Initially it generally followed an alternating home-and-away pattern, except that if a seventh game was possible, its site was determined by coin toss prior to the sixth game. In 1924 the Series began using a 2-3-2 format, presumably to save on travel costs, a pattern that has continued to this day with the exception of a couple of the World War II years when wartime travel restrictions compelled a 3-4 format (used in 1943 and 1945, but not in the 1944 series, which was all in the same stadium in St. Louis). From the start of the 2-3-2 format through the 2002 season, home-field advantage generally alternated between leagues each year. Prior to the 1994 strike, the National League champion received home-field advantage in even-numbered years and the American League champion in odd-numbered years; these were reversed for 1995-2002 (because 1994 would have been the NL's turn to have home-field, but the World Series was cancelled by the aforementioned strike). That changed starting in 2003.
The 2002 All-Star Game had ended in a tie, much to the displeasure of both fans and sportswriters who complained about a lack of intensity and competitiveness on the part of the players. This hit especially close to home for Commissioner Bud Selig, as the game had been played in his home city of Milwaukee, Wisconsin. In response, to give some real meaning to the game, in 2003 MLB began assigning home-field advantage in the World Series to the winner of that year's All-Star Game, which is typically held in mid-July.
Following the acceptance of a new collective bargaining agreement after the 2016 season, home-field advantage in the World Series will no longer be tied to the outcome of the All-Star Game, but will instead go to the team with the better regular-season record. 
Until 1998, the LCS alternated home-field advantage with a 2-3 format in the best-of-5 era (1969-84) and a 2-3-2 format when it went to best-of-7 (1985-present). Since 1998 the team with the better record has had this advantage, except that in no case can the wild card ever secure the extra home game, regardless of regular-season records.
Until 1998, the Division Series rotated which of the three division champions would not have home-field advantage, with the wild card never having it. Now the two division winners with the best records in each league have home field, with the least-winning divisional winner and the wild card not having home field. The DS used a 2-3 format until 1998 and now uses a 2-2-1 format. This is seen as a more fair distribution of home-field advantage because previously under the 2-3 format, the team hosting the first two games had absolutely no chance of winning the series at home. With the current 2-2-1 format however, both teams have the home-field advantage in a sense. While one team gets to host three games (including the critical first and last game), the other team does get two chances out of three (games 3 and 4) of winning the series on its home field.
With the adoption of the expanded playoff format in 2012, the five-game Division Series began with two home games for the lower seeds, followed by up to three home games for the higher seeds. This one-year change eliminated a travel day prior to a decisive Game 5 of a Division Series and was necessary because the 2012 regular-season schedule was announced before the agreement on the new postseason was reached. For 2013, the Division Series returned to the 2-2-1 format that was used from 1998 to 2011.
There are three factors that determine the actual amount of bonus money paid to any individual player: (1) the size of the bonus pool; (2) their team's success in the season/post-season; and (3) the share of the pool assigned to the individual player.
There is a separate pool for each series - the Wild Card games, the Division Series, the League Championship Series, and the World Series. The players' bonus pool is funded with 60% of the gate receipts for each of the Wild Card games, the first three games of each Division Series, the first four games of each LCS and the first four games of the World Series; limiting the funding for the pool to these games, the minimum number in each series, removes incentive to extend the series for merely fiscal sake. The value of the gate is determined by the size of the venues, the amount of high-priced premium seating in the venues, the number of games played in the series and whether the games sell out. Ticket prices for each series are set by MLB, not the home teams, so they are relatively uniform across baseball.
The World Series winner gets 36%, the World Series loser gets 24%, both League Championship Series losers get 12%, the four Division Series losers get 3.25%, and the two Wild Card playoff losers get 1.5%.
The division of the team's share of the pool is voted upon by the players who have been on the team during the entire regular season, in a meeting chaired by their union representative. This meeting follows the trade deadline on July 31. Players who have been with the team for the full season automatically receive a full share. At the meeting, the full-season players vote on whether anyone else--including players who have not been with the team for the full season, coaches, and trainers--is to be granted a full share, less than a full share, a cash award, or no share. After the World Series, the pool of money is split according to the shares determined in the vote. There is no limit to the number of shares that may be granted, but a greater number of shares dilutes the value of each share, and consequently the amount each player is awarded.