Markku Veijonsuo (b. 1961) is one of the most important jazztrombonists in Finland who hasn't let the scale of his instrument to limit his way to express himself musically. The first jazzbands for Veijonsuo were traditional big bands, for example Settlement Big Band, Pori Big Band and Espoo Big Band, but quickly Veijonsuo's creative use of his instrument and the merits as a great lead-trombonist were noticed and in 1984 Veijonsuo was appointed as the leader of the trombone section in UMO Jazz Orchestra.

Besides UMO and the jazzstudies at the Sibelius Academy, Veijonsuo had time to play in the late-1980s and early-1990s in i.a. Esko Heikkinen's Super Brass, Jukka Linkola's Tentet and on several albums of many pop- and rockartists. Veijonsuo's own groups at that time were Markku Veijonsuo Quartet and Veijonsuo-Priha Punishment together with trumpetist Antero Priha. In 1994 Veijonsuo graduated from the Sibelius Academy with a Master's degree and has ever since taught trombone at the jazz department.

In the mid-1990s Markku Veijonsuo started to prepare the "solotrombone operation" where he modified the sound of the trombone and a didgeridoo with modern soundprocessors into a multi-layered soundjourney. Using the technique isn't though the main purpose of the project: Veijonsuo's jazzambient has also a melodic content and a musical story. The debut concert of the solo project was in December 1997 in Helsinki and the next year Veijonsuo performed his operation also at Musiikin Aika Festival in Viitasaari and at Tampere Jazz Happening. The project was also recorded and released as an album Karakara (Silence 1998) that got extremely good feedback from the critics in Finland and abroad. In 1999 Veijonsuo did a Vapaat äänet -tour in Finland with accordeonist Kimmo Pohjonen.

The solotrombone operation has been a successful project for Veijonsuo and he has been performing the project abroad as well. Thanks to the grant given by National Council for Music, Veijonsuo was able in 2000 to concentrate, besides his soloproject, also to his new trio, a band formed by Veijonsuo, bassist Lasse Lindgren and drummer Mika Kallio. The group used some elements from Veijonsuo's soloprojects in it's music  and performed also compositions from Veijonsuo's musical partner, Markus Fagerudd. In 2000 Markku Veijonsuo Trio recorded a radiotape for YLE and did a Vapaat äänet -tour in Finland.

Veijonsuo rearranged some parts of his solo project also for the 25th Anniversary Concert of UMO Jazz Orchestra in 2000. In the 21st century trombonist has also worked a lot as the conducter of UMO. His love for sound systems and studio technology has been growing in the years and besides his own music, also many other artists have recorded their albums at Veijonsuo's Varistoteles Studio, like saxophonist-flutist Kari "Sonny" Heinilä's album Mosaique and trumpetist Mikko Pettinen's MP4's second album Follower.