Founded in 1954 as Club Deportivo Universidad, and they play their home games at Estadio Olímpico Universitario, which seats over 72,000 spectators.

[11] The team is also known for its youth development system, which has produced international players such as Hugo Sánchez, Manuel Negrete, Luis Flores, Miguel España, Claudio Suárez, Luis García, Alberto García Aspe, David Patiño, Jorge Campos, Braulio Luna, Gerardo Torrado, Francisco Fonseca, Efraín Juárez, Héctor Moreno, Pablo Barrera, Israel Castro, Eduardo Herrera and Jesús Gallardo.

The dean of the university, Luis Chico Goerne, made the first attempt to affiliate a representative of UNAM with the top football Mexican championship of the day, filing a petition to join the Liga Mayor de Fútbol Professional del Distrito Federal.

By the 1940s, the dean Gustavo Baz Prada assigned the task to prepare the UNAM team to Rodolfo "Butch" Muñoz, then player of Club España.

In August 1954, the Club Universidad was accepted as a member of the Segunda División, in those days the second tier division of professional football in Mexico.

This achievement was accomplished with the support of the dean Nabor Carrillo and Guillermo Aguilar Alvarez Sr., a benefactor of the club.

The match ended, the students rushed the pitch, and honored its team by carrying them off the field on their shoulders—this was the first step towards the consolidation of the club.

The following day, dean Ignacio Chávez Sánchez congratulated the team when he met with them: Octavio Vial (manager), and players: Homero Villar, Raúl Chanes, José Antonio "La Espátula" Rodríguez, Roberto Cuevas, Rafael Ramirez Jimenez, Alfredo Echávarri, José Ruiz, Carlos Gutierrez, Alfredo "Tito" Zenteno, José Luis "El Chango" Ledezma, Antonio Sámano, Jorge Gaitán, Guillermo Vázquez Sr., José Luis González "La Calaca", Lorenzo Garcia, Carlos Calderón de la Barca, Manuel "Manolo" Rodríguez, Edmundo "El Poli" Pérez, and Gustavo "El Gato" Cuenca.

After two years under the management of Alfonso "El Pescado" Portugal, the Spaniard Ángel Zubieta took the reins of the team.

The first half of the decade was marked by the arrival of three of the most important foreign players in the existence of the club; the Peruvian Juan José Muñante, the Serbian Velibor "Bora" Milutinović, and the Brazilian Cabinho.

They arrived to join a solid base of native-players such as Miguel Mejía Barón, Héctor Sanabria, Arturo Vázquez Ayala, José Luis "Pareja" López, and Leonardo Cuellar.

In 1978, Club Universidad would signed Ricardo "Tuca" Ferretti, a player that will prove to be vital for the team in the coming decade.

This decade also marked the national recognition of the work performed by the club, and the revolutionary and dynamic style of play that helped Mexican football overall.

The stability and discipline that Ferretti brought to the team paid off as the Pumas climbed out of the relegation zone and reached a final in 2007 against Atlante, which they lost 2–1 on aggregate.

After the club's inability to make it to the play-offs in Clausura 2016 and failing to reach the semifinal for Copa Libertadores 2016 Guillermo Vasquez was once again sacked as head coach in May 2016.

In the 2020 Apertura, Pumas reached the final, losing to Club Leon on a 3-1 Aggregate with coach Andres Lillini after sacking Michel the season prior.

Mohamed's time on the bench did not last long as he resigned shortly after Pumas' elimination in the semifinals of the 2023 Apertura to Tigres.

In the 1980s the rivalry grew when Club América defeated Universidad twice in the league finals, both times with controversial refereeing decisions.

A new generation of players from the youth system grew up hating their adversaries; this decade is also marked by the birth of Las Barras Bravas, who supported both sides but had a much longer background story of rivalry.

The rivalry with Cruz Azul comes out of the fact that both clubs are located in Mexico City, and they have played many important matches, including two league finals, recently the name of this game is the "Clásico Metropolitano” or “Derby central" because both teams were born in states that are in the central part of Mexico Pumas UNAM and Leones Negros are old rivals.

One major encounter these two clubs have had with each other was in the 1976-77 Primera División final, when Pumas UNAM beat Leones Negros to achieve their first title.

But over the years the rivalry has died down due to the Leones Negros going through a state of decline and relegated to the Segunda División.