After completing his advanced studies in flute at the Superior Conservatory of Music of Aragon, he began his studies in traverso at the Escola Superior de Música de Catalunya (ESMUC) under the guidance of Marc Hantaï, with whom he continued studying later at the Schola Cantorum Basiliensis. Additionally, he regularly received classes in classical and romantic flute in Paris from flutist Amélie Michel (Orchestre des Champs Elysées).

Luis Martínez expanded his knowledge in traverso and chamber music, receiving instruction from prominent figures in early music such as Barthold Kuijken, Wilbert Hazelzet, Kate Clark, Rachel Brown, Lisa Beznosiuk, Ashley Salomon, Valérie Balssa, Agostino Cirillo, Hopkinson Smith, Jesper Christensen, Olivier Baumont, Kristian Bezuidenhout, Manfredo Kraemer, François Fernandez, Amandine Beyer, Leila Schayegh, Emmanuel Balssa, among others.

As a founding member and artistic director of La Guirlande – a group dedicated to performing music from the 18th and 19th centuries with the flute playing a prominent role – Luis Martínez has collaborated with orchestras and ensembles such as: the Orchestra of the Age of Enlightenment, Concert des Nations, Les Musiciens du Prince Monaco, Collegium 1704, Bach Akademie Luzern, Forma Antiqva, Els Mvsics de sv Altesa, The Bach Collektiv, Ensemble Cristofori, Ensemble Els Elements, Cardinal Complex, Chiave d'Arc, Orquestra Barroca Catalana, Ensemble Phaedrus, Svapinga Consort, and Orchester Le Phénix, among others. He has performed in important venues in Spain, France, Germany, Switzerland, Austria, the Netherlands, Poland, Scotland, and Estonia.

He has recorded albums with various ensembles for labels such as Decca, Glossa, Passacaille, Vanitas, Coviello Classics, and Orpheus. With his group La Guirlande, he has recorded two albums dedicated to the recovery of Spanish music from the 18th century, titled "Spanish Travelling Virtuosi, Vol. 1" and "Cristal bello", featuring up to 10 works of heritage recovery.

He served as a flute teacher from 2010 to 2013 at the Conservatorio Elemental de Música in Zaragoza. Since 2021, he has been a professor of traverso at the Escola Superior de Música de Catalunya.

La Guirnalde