Luís Costa began his musical studies at the age of 8, with Zhuang Xiao Hua. A few years later, he continued with his current teacher and greatest inspiration, Álvaro Teixeira Lopes. In 2012, he studied at the University of Stuttgart under the guidance of Friedemann Rieger, where he completed his course with top marks. He has won prizes at a number of competitions, such as: the Mesnil des Arts International Competition, the Alto Minho Iberian Competition, the Saint Cecilia International Competition and the Young Musician's Award (Chamber Music).

He has performed in recitals all over the country and abroad, of note being his recent performances in Germany (Darmstadt, Reutlingen, Romrod, Filseck), where reviews described him as a “musically sophisticated pianist” (in the Fuldaer Zeitung). He has also performed in cities such as Girona, Rome, Johannesburg, Pretoria, Cape Town, Ottawa, Toronto, Montreal, Harare, Windhoek, London, Frankfurt, Darmstadt, Stuttgart, Léon, Madrid, Barcelona, Bergen and Alkmaar, as well as concert halls like the Sala Suggia in Casa da Música, the Glenn Gould Studio, the Ciudad de Léon Auditorium, Centro Cultural de Belém, etc. His participations in festivals include the Sant Pere de Rodes Festival, the Percursos da Música Festival, the St. Mesnil des Arts Festival, the Campo Alegre Theatre New Talents Cycle, the Musique in Vallée du Tarn Festival, the Zaragoza Young Performers' Cycle, the Besálu Music Festival and the Hammerklavier Series.

In September 2013, he was selected to take part in all the Beethoven concerts and had the opportunity to work with Maestro Bruno Aprea and his class, and the Málaga Youth Symphony Orchestra. He has also done solo performances with the Beiras Philharmonic Orchestra, the Maia Chamber Music Orchestra, the Porto Military Band and the Lusitanae Ensemble. Currently, he is in regular contact with pianist Joaquín Soriano in Madrid, who is also a major source of inspiration.

He dedicates part of his time to chamber music and has worked with musicians such as António Meneses, Lluis Claret, Hans-Peter Stenzl and António Chagas Rosa. He works intensively in a duo with his brother, cellist Fernando Costa. His upcoming projects include concerts in Brazil and China and recording a CD of previously unpublished Portuguese music at the Calouste Gulbenkian Foundation, with backing from the GDA Foundation. He is on the Doctoral programme at the University of Aveiro, where he taught in 2016/2017.

He has recorded for RTP and Antena 2, CHIN radio and NBC television. He is represented by the KNS Artists agency. He has recorded CDs with works by Scarlatti, Schumann and Chopin for the KNS Classical label.