In 2016, The Daily Telegraph ranked him as the third best male clay-court player of all time, behind Rafael Nadal and Björn Borg.

Historical and statistical studies presented in 2015 by Argentinian journalist Eduardo Puppo and Romanian mathematician Marian Ciulpan concluded that Vilas should have been No.

The ATP and its chief executive at that time, Chris Kermode, although not refuting the data, decided not to officially recognize Vilas as No.

[14]Raised in the seaside resort of Mar del Plata, Vilas was a left-hander and played his first tour event in 1968.

In addition, he won seven Grand Prix Super Series titles (1975–80), the precursors to the current Masters 1000.

The highest point during this run was winning the last US Open played at Forest Hills against Jimmy Connors 2–6, 6–3, 7–6(7–4), 6–0 in a match where Vilas surprised his American rival by attacking the net.

Both his winning streaks were terminated in October 1977 by Ilie Năstase in the final of the Raquette d'Or tournament.

In that best-of-five-set final, Vilas dropped the first two sets by 6–1, 7–5 and then retired in protest of Năstase's use of a spaghetti racquet.

[19] After that he won a further 28 matches in a row with titles at Tehran, Bogotá, Santiago, Buenos Aires (all on clay), and Johannesburg (hard).

[30][31][32] Argentine journalist Eduardo Puppo and Romanian mathematician Marian Ciulpan investigated the 1973–78 period records, and delivered a detailed report with more than 1,200 pages in which they came to the conclusion that Vilas should have been ranked No.

[20][34] In October 2020, Netflix released a documentary about the controversy titled Guillermo Vilas: Settling the Score.

[14] In 1983, the Men's International Professional Tennis Council on June 7 suspended Vilas for one year and fined him $20,000, having found that his manager and coach, Ion Tiriac, on the player's behalf, had accepted about $60,000 in appearance money from tournament promoters.

[17] Vilas was in the stands at Flushing Meadows to cheer on his countryman, Juan Martín del Potro, who beat Roger Federer in an upset in the 2009 US Open final.