R. Katilius was born in a family of doctors (Kazys and Vanda Katilius) on the 16th of March in 1947, Vilnius. From 1953 to 1964 he was a pupil in the Vilnius Secondary Art School (now The National M. K. Čiurlionis School of Art). From 1960 he was taught to play the violin by professor A. Livontas. In ninth grade, he played his first recital in the grand hall of the school.

In 1964 he was accepted into the Lithuanian National Conservatory (now the Lithuanian National Academy of Music and Theatre), where he continued to learn violin from professor A. Livontas. From 1965 to 1970 he studied in Moscow’s P. Tchaikovsky’s State Conservatory, in the violin class of professor I. Bezrodnas. In 1972 he received a postgraduate degree from this school.

In September of 1970, R. Katilius performed his first official concert with an orchestra in Tauragė. The musician considers this concert to be the beginning of his creative work.

He became known internationally after successfully performing in the 1970 Helsinki and 1972 Montreal violin contests. He played the first violin in the quartet of Moscow conservatory postgraduate students, winning contests in Belgrade (1971) and Bratislava (1972). From 1972 to 1975 he played first violin in the Moscow Philharmonic string quartet.

While touring Siberia in 1974, R. Katilius received a telegram informing him of the death of professor A. Livontas and asking him to return to Vilnius and take over the students of the late musician. He returned and tutored over 60 violinists in Lithuania, while continuing to play at least 100 concerts every year. Well known students include L. Binderis, D. Dikšaitis, R. Kiškytė, R. Griciūtė-Kubilienė, Z. Levickis, D. Suraučiūtė, I. Belickaitė, M. Švėgžda von Bekker, R. Vosiūlytė and others. In 1987 R. Katilius became a professor.

Both musicologists and composers agree that when the violinist returned to Lithuania, people were inspired to write music for the violin. Several composers have dedicated pieces to the artist: O. Balakauskas, F. Bajoras, P. Dikčius, M. Kupfermanas, J. Radzinskis. The violinist was the first to perform and sometimes even edited works by E. Balsys, V. Barkauskas, J. Bašinskis, P. Dikčius, V. Jurgutis, V. Laurušas. R. Katilius edited the 3rd concert for solo violin by E. Balsys, dedicated to the memory of A. Livontas.

He has performed multiple times with pianist L. Lobkova. On the 11th of March 1992, they performed together in New York’s Carnegie Hall. Both musicians have performed in prestigious international music festivals.

In 1995 he performed a concert celebrating the 25th anniversary of his creative work, where he played W. A. Mozart’s concert for violin no. 5 A-major as well as concerts for violin and orchestra by M. Bruch and P. Tchaikovsky.

On an evening in 1997, he performed a concert dedicated to his 50th birthday, playing a concert for two violins by J. S. Bach together with his daughter R. Katiliūtė as well as concerts by J. Brahms and D. Shostakovich together with the Lithuanian National Symphony Orchestra, conducted by G. Rinkevičius.

The famous violinist died on the 4th of March 2000, in Bad Kisingen (Germany).

The performer has received several awards:
1979 - Lithuanian Soviet Socialist Republic Distinguished Artist Award.
1981 - Lithuanian Soviet Socialist Republic State Prize.
1985 - Lithuanian Soviet Socialist Republic Artist of the People.
1995 - Lithuanian National Prize.
1998 - Lithuanian Grand Duke Gediminas 3rd order award.