Vesala is a Sibelius Academy graduate, having studied in the Nordic Master in Jazz programme under the instruction of today's leading jazz trumpetists, such as Tim Hagans, Gerard Presencer, Laurie Frink and Peter Asplund. A creative and experienced composer, Vesala has written original music for nearly two decades for ensembles of all sizes, ranging from quintet to big band. His original compositions contain catchy melodies supported by lush harmonies and the rhythmic layers of Afro-American heritage of jazz. As a trumpet player, Vesala's style is influenced by Miles Davis, Freddie Hubbard and Woody Shaw, in addition to the more modern stylings of Dave Douglas and Kenny Wheeler.

Martti Vesala is the leader of two jazz quintets: Martti Vesala Soundpost Quintet is comprised of crème de la crème of young finnish jazz musicians. The group's music consists entirely of Vesala's compositions, reflecting his long time admiration of Wayne Shorter's music and the groove of the 1960's Miles Davis Quintet. The group's debut album "Helsinki Soundpost" was released September 2016 by the german Ozella Music. Soundpost Quintet's second album "Stars Aligned" will be released in April 2018.

Vesala is also the leader of jazz group Maratone Quintet. The band's music reflects the members' eclectic tastes in music, combining Nordic jazz with influences from post-rock to the groups of Dave Douglas and Esbjörn Svensson. Maratone Quintet has performed extensively in Finland and Estonia since 2005, playing at numerous jazz-clubs, concert halls and jazz festivals. The quintet has appeared at the Dølajazz 2010 festival, organized in Lillehammer, Norway. In 2010, they represented Finland in the finals of the Getxo International Jazz Group Competition in Spain. Maratone Quintet has produced and recorded two albums: "Setting Out" (released by Free Agent Records 2008) and "Finding the Way" (Prophone 2012).

Vesala's big band compositions have been performed by UMO Jazz Orchestra, Klüver's Big Band (Aarhus, Denmark), The Big Band of The Royal Academy of Music (Stockholm, Sweden) and Jyväskylä Big Band. He has been a finalist of the Esko Linnanvalli Big Band composition competition 3 times: in July 2011 with an original composition "Subconstellation", in November 2013 with "Rhododendron" and in 2015 with "Piper's Park".

Vesala also works actively as a freelance musician with such groups as Njet Njet 9, Nicole Willis And The Soul Investigators and Aiyekooto And The Afrobeat International. He also performs occasionally in the ranks of UMO Jazz Orchestra, Espoo Big Band, Vantaan Viihdeorkesteri (Vantaa Pops Orchestra), TUMO Orchestra, Sibelius Academy Alumni Big Band, musicals produced by the Helsinki City Theatre and numerous other projects.