In 1965, the football team was promoted to the Primera División Argentina for the first time. The team has played there for many years, alternating with periods in the second division. Unión's supporters are called "unionistas", "tatengues", while the squad is usually nicknamed "El Tate". The colours of the club consist of red and white vertical stripes.

In 1979 Unión played the final matches of the Nacional championship, but lost at the hands of River Plate, because the goal scored by River in the first match (with a final score of 1-1) ended up in an average over Union according to the away goals rule applied to that tournament.

The most famous footballers who played for Unión are Leopoldo Luque, World Cup winner with Argentina in 1978, and Nery Pumpido, the goalkeeper of the national team that won the World Cup in Mexico 1986.

Apart from football, basketball is the foremost sport practised at the institution, with Union's team currently in the third division. Carlos Delfino is its most famous basketball player.