Uniform numbers are on backs, and sometimes both, fronts and backs of uniforms of baseball players, coaches, managers, and most baseball team personnel. Numbers are commonly used to identify one player from another.
In the major leagues, the Cleveland Indians briefly introduced numbers worn on their players' sleeves in 1916. The St. Louis Cardinals tried something similar in 1922, but also discontinued it after a short time. So it was the New York Yankees who were the first team to put numbers on the back of the uniforms, announcing their plan in January of 1929. Cleveland immediately followed suit, and since the Indians' opening game was played before the Yankees' that year because of a rainout, they were the first team to actually wear numbers in a game. The Yankees issued their uniform numbers according to their players' place in the batting order. Thus, Babe Ruth, who batted third, was number 3, and Lou Gehrig, the clean-up hitter, was number 4.
One of the highest honors a team can pay to one of its players is to have his uniform number retired, i.e. not used by any other player after him. One uniform number, 42, is retired throughout major league baseball in honor of Jackie Robinson, the pioneer of baseball's integration. That number is worn by all players once a year, on "Jackie Robinson Day", however, in tribute to Robinson. There is a movement asking to have similar treatment reserved for number 21 worn by Hispanic pioneer Roberto Clemente, but Major League Baseball has not acquiesced.
The main section of this Baseball-Reference site has uniform numbers listed on its player and team pages. In addition, the Bullpen has an article about each individual uniform number that has commonly been issued to players. Traditionally, players and other uniformed personnel wore numbers in the lower end of the range, with numbers in the 40s the upper limit, but this changed gradually starting in the last couple of decades of the 20th century, with unusual numbers being worn more and more commonly. On some teams, notably the Yankees, all of the lower numbers have been retired anyway, making them unavailable. As of the start of the 2020 season, every number from 0 to 99 (as well as 00) had been issued to at least one player in major league history, except for three. The last remaining exception was 89, after players wore numbers 86 and 92 for the first time in August of that year, and it too was assigned to a player later that month.
- Mike Petriello: "Every uniform number ever, ranked by value: The most valuable jersey number is ...", mlb.com, July 15, 2020. 
- Manny Randhawa: "Baseball jersey bingo: One number left", mlb.com, August 19, 2020.