The left-sided specialist, who was born in the Azores, Eliseu is comfortable either at full-back or in a more advanced position on the wing. He started out at Maritimo Angra, but moved to the mainland in 2002 with Belenenses, who loaned him to second-division side Varzim for a spell. In 2007, he joined Malaga in Spain and became a key figure at the club over seven years, despite having stints at Italian club Lazio and Real Zaragoza in between. In 2014, he signed for Portuguese champions Benfica, where he won several league and cup titles.

Eliseu has been part of Portugal's senior national set-up since making his international debut in 2009 in a friendly against Estonia, although he has never been a fixture in the squad. He did not travel to the 2014 FIFA World Cup Brazil™, but was recalled for UEFA EURO 2016, making two appearances at the tournament.