Nuñez was born in 1971 in the city of Vigo and began playing the bagpipes when he was eight years old. In his early teens, he was invited to play with the Festival Orchestra of the Festival Interceltique de Lorient in Brittany. He studied the recorder at the Royal Conservatory in Madrid, Spain and quickly gained stature as a young virtuoso. He met Paddy Moloney of The Chieftains and performed with the band two years later, becoming referred to as the "7th member" of the band. He appeared on their Grammy-winning Santiago, which focused on Galician music and included other artists such as Los Lobos and Linda Ronstadt.
He has become an integral part of the Galician Celtic music scene, and has collaborated with Ry Cooder, Sinéad O'Connor, The Chieftains, Altan and La Vieja Trova Santiaguera. His most renowned album was 1996's A Irmandade Das Estrelas, which sold an unprecedented 100,000 copies, and included collaborations with Nightnoise, Luz Casal, Tino di Geraldo, Tríona Ní Domhnaill and Mícheál Ó Domhnaill, Kepa Junkera, Ry Cooder, The Chieftains, and Dulce Pontes. He has since moved on to including elements of Berber music and flamenco, as well as more pronounced Celtic, especially Breton, influences. He was a key collaborator in Tamiya Terashima's soundtrack from the film Tales from Earthsea (Gedo Senki), released in July 2006. He also released an additional album, titled Melodies from Gedo Senki, which included new Gedo Senki OST tracks along with new tunes by Carlos himself.
On his 1999 album Os Amores Libres, he collaborated with French producer Hector Zazou.
He continues to tour the world playing in large and small venues.