Violinists Ysaÿe, Fritz Kreisler, George Enescu, Mischa Elman and Jascha Heifetz, as well as composers such as Igor Stravinsky and Jean Sibelius, held Quiroga's artistry in great regard.

In 1937, Quiroga was involved in a traffic accident in New York City, which left him with a paralysed arm and ended his playing career.

[1] In June 1904, he was awarded a grant to study at the Madrid Royal Conservatory with José del Hierro,[2] an exponent of the Franco-Belgian school of violin playing who was considered the leading Spanish violinist of his time.

He also associated with George Enescu and Eugène Ysaÿe, and learned some of Kreisler's compositions, while enjoying the friendship of Manuel de Falla, Joaquín Turina, Pablo Casals, Darius Milhaud,[9] the cellist Juan Ruiz Casaux and the French pianist Marthe Lehman, a fellow student at the Conservatoire.

[1] On 4 July 1911, aged 19, Quiroga won the Conservatoire's Première Prix nommé, awarded by a jury that included Gabriel Fauré, Kreisler, Thibaud, Boucherit, Lucien Capet and Martin Pierre Marsick.

[1] He made Paris his base, and he associated there with musicians such as Paul Paray, Manuel Infante, Joaquín Nin and Ricardo Viñes, along with Casals, Falla, Turina, Milhaud and others.

[1] At the start of World War I, he was giving concerts in Austria with José Iturbi when he was accused of espionage and jailed for a short time, until the intercession of the Spanish king Alfonso XIII secured his release.

[1] He made four highly successful tours of the United States and Canada during the war years, starting in 1914, again including Cubiles and Casaux.

[1] He refused a fifth planned American tour when his friend Enrique Granados drowned in the English Channel while returning from New York City in 1916, a victim of a German submarine torpedo attack.

After the war, he returned to Spain and received a huge public reception at the Palau de la Música Catalana in Barcelona.

[1] In 1923 Eugène Ysaÿe dedicated the last of his Six Sonatas for solo violin to Quiroga, the other dedicatees being Joseph Szigeti, Jacques Thibaud, George Enescu, Fritz Kreisler and Mathieu Crickboom.

[1] He made more tours of America in 1933 and 1937, where he gave recitals with Mischa Levitzki and José Iturbi, and concerts with the New York Philharmonic under the baton of George Enescu (playing Édouard Lalo's Symphonie espagnole in February 1937).

[1] In 1940 he made an extensive series of caricatures of his friends: Fritz Kreisler, José Iturbi, Eugène Ysaÿe, Pablo Casals, Carlos Chávez, Andrés Segovia, Arthur Rubinstein, Lucien Capet, Ricardo Viñes, Jacques Thibaud, and others.

He became virtually confined to a sanatorium in Madrid, and in 1959 moved back to his home town of Pontevedra, where he was cared for by his second wife Maria Eladia Galvani Bolognini (whom he called Gigi).

The pieces include works by Albéniz, Falla, Kreisler, Sarasate, Wieniawski and others, and importantly, four of his own compositions: Segunda Guajira, Danza española, Rondalla, and Canto amoroso.

There is also a memorial bust in Pontevedra, the work of the sculptor Francisco Asorey, and in the city square is a full-size statue of him shown playing the violin to a group of friends seated around him.

In his centenary year 1992, the City Museum of Pontevedra organized a series of commemorative events such as an exhibition of his paintings and drawings and some musical homages.

[1] His biography was published in 1993 by Fernando Otero Urtaza, and an article by Tully Potter in the special Iberian issue of The Strad in July 1998 traced his career.