Ján Slávik studied playing the violoncello at Bratislava Conservatory under Gustáv Večerný and Karol Filipovič and at the College of Performing Arts (VŠMU) in Bratislava under Jozef Podhoranský. He studied chamber music in Vienna at Hochschule für Musik und Darstellende Kunst under Franz Samohyl and Günter Pichler. In the year 1992 he got a ArtD. title at VŠMU where he has been working as a university teacher since 1993. In the year 2012 he was appointed a university professor  in  music art by  the President of  the Slovak Republic.
He took part in several  interpretation courses (Weimar, Kerkrade, Bayreuth, Piešťany) and is a holder of numerous awards: the Prize for the best interpretation of contemporary music (Pražská jar / Prague Spring 1983), the Prize of music criticism (Mladé pódium /Young  Platform Karlove Vary 1991). In the year 2001 he was awarded the Prize of criticism of  the Slovak Musicological Association and in the year 2009 he got the Prize Sebastian for his extraordinary contribution to the heritage of Johann Sebastian Bach´s  work for contemporaries. Ján Slávik is one of the founders of  the Moyzes Quartet (1975), which  in the years 1986-2005 was the chamber orchestra of the Slovak Philharmonic. Since the year 2006 the Moyzes Quartet was the chamber ensemble of the town Modra. Since the year 2008 it has been the chamber ensemble of the town Skalica.  In the year 2015 Quartet won The Award of the Tatra banka Foundation for Art and also the Award of the Minister of Culture for the Art. He is a co-founder of the civic-associaton Albrechtina (2010). With the Moyzes Quartet Ján Slávik has given concerts in almost all European countries, Japan, the USA ,Canada, Marocco, India, Cuba, etc.,  and has recorded more than 40 compact discs. As a soloist he has recorded 15 CDs. Last CDs are Dvořák´s  violoncello concert B-minor op.104 with Bratislava Symphonics and Zeljenka´s cello concert with Slovak Philharmonic. He was the first performer of cello concerts of Jozef Kolkovich, Ladislav Kupkovič and Ilja Zeljenka, which were dedicated to him. He performed with leading Slovak orchestras, with the orchestra Simfoniette – de Barcelona and Salzburg Chamber Orchestra. He has given concerts in Germany, Spain, France, Denmark, Austria, the Czech Republic, Poland, Russia, in Ukraine and in Malta.  In the year 2006 Ján Slávik was a solo-violoncellist in the Symphonic Orchestra of the Slovak Radio. Since the year 2008 he has been the concertmaster of the violoncello section in the Slovak Philharmonic. In July 2012 he performed as a soloist in Dvořák´s  violoncello concert B-minor  op. 104 with the Slovak Philharmonic in Tokio.
As the first Slovak interpreter he, together with Daniela Varínska, introduced  complete work of Ludwig van Beethoven for  the piano and violoncello ( sonatas and  variations ), which were issued on three compact discs by Diskant music publishing house. For Diskant he also recorded 3 CDs of  Bach´s solo suites and sonatas. Ján Slávik also devotes himself to interpretation of  contemporary music and several Slovak composers ( Iršaj, Kupkovič, Zeljenka, Berger ...) dedicated their  musical works to him.  In the years 1997 – 2004 he was a member of the string trio Amade. Since 2005 he is a member of the Berger Trio. His conductors´ partners have been Adolf Vykydal, Bystrík Režucha, Róbert Stankovský, Karol Kevický, Ondrej Lenárd, Leoš Svárovský, Bohdan Warchal, Jack van Steen, Hideaki Umeda, Harald Nerat, Joan Luis Moraleda, Stephen Somary, Harvey Bordowitz, Jerzy Swoboda, Juraj Valčuha. He gave concerts in all significant home music festivals, abroad he performed in festivals Wurzer Sommerkonzerte (DE ), Mladé pódium/Young Platform Karlove Vary (CZ ), Festival Haute-Savoi ( FR), Vendrell – Festival international de Musica Pau Casals ( ES), International Music Festival Ljubljana (SI ), Sommerkonzerte Langenargen ( DE ), Festival Est-Oest Die ( FR ), Neue Musik Hannover ( DE ), etc. He regularly leads master interpretation courses ( Dolný Kubín, Komárno, Žilina ) and is a member of juries  in home and international music competitions. He is the founder of the international art festival Hudba Modre and the Slovak art festival Hudba Trnave as well as  the international festival Divergencie in Skalica. Ján Slávik regularly cooperates with radio and television and records for music publishing houses Diskant, Marco Polo, Naxos, TUTL and Classico.