They played in the second division from 1956 to 1964, and from 1972 to 1976, when they won their first title; the Argentine second division winning them promotion to the Primera División . Platense achieved cult status in the late 1970s as they repeatedly staved off relegation through a series of last-day miracles. Platense survived at the top level of Argentine football until they finally succumbed to relegation in 1999.
This was the beginning of a steep decline in the clubs fortunes, they were relegated to the regionalised third tier Primera B Metropolitana at the end of the 2001/02 season. On May 17, 2006, Platense won their second title and were promoted back to the argentine second division Nacional B.
Historically, Platense's fan base is drawn from the towns of Vicente López, Olivos and Florida, and the neighborhoods of Villa Urquiza and Saavedra in the city proper. The club is cited in Bioy Casares's El Sueño de los héroes ("Dream of Heroes" ISBN 0704326345). In real life, Roberto Goyeneche was a most notable fan.
The club nickname is calamar (squid) after the journalist Palacio Zino said that the team moved "like a squid in his ink".