Note: As part of MLB's health and safety protocols during the COVID-19 pandemic, each club will have a 30-man roster for the first two weeks of the 2020 season, 28 for the next two weeks, and 26 for the remainder of the season. Teams will submit lists of 60 players eligible to play in 2020 -- the 40-man roster plus a "taxi squad" of 20 players. Rather than a 10-day injured list for position players and 15-day injured list for pitchers, there will be a 10-day injured list for all players in the shortened season. The 60-day injured list will be reduced to 45 days. Instead of July 31, the Trade Deadline will be Aug. 31. Players must be on a club's roster by Sept. 15 in order to be eligible for postseason play.
In a typical season, any player who is on the 40-man roster or 60-day injured list as of 11:59 p.m. ET on Aug. 31 is eligible for the postseason.
Those on the restricted list at that point are also eligible if they haven't been suspended for performance-enhancing drugs during that season. (All players who have served a suspension for PEDs in a given season are ineligible for postseason play that year.)
A player who doesn't meet said criteria for postseason eligibility can still be added to a team's roster in the postseason via petition to the Commissioner's Office if the player was in the organization on Aug. 31 and is replacing someone who is on the injured list and has served the minimum amount of time required for activation. (For example, a player on the 10-day injured list who has been on it for at least 10 days, or a player who has been on the 60-day injured list for at least 60 days.) Players who are acquired in September or after are ineligible.
Postseason roster rules
Teams submit a 26-man roster (it was 25, prior to 2020) prior to each round of the postseason comprised of postseason-eligible players. A club may request permission from the Commissioner's Office to replace a player who is injured during the course of a series, but that player is then ineligible for the rest of that round and the subsequent round, if there is one. A pitcher may be replaced only by another pitcher, and a position player only by another position player.
Teams carry extra players throughout the postseason in the event of injuries, and those players, as well as players on the injured list, can be in the dugout during games, within reason.