K Tríó was started up by Kristján Martinsson in January 2008 to perform his compositions in his final recital at Icelandic Musicians Union School of Music. He chose, with him, Petur Sigurdsson on bass and Magnús Trygvason Eliassen on drums. After this cooperation the trio decided to carry on, compose and perform more together. They took part in Reykjavik Jazz Festival in August of the same year holding a concert in Idno. In September K Trio represented Iceland in The Young Nordic Jazz Comets in Copenhagen. They won the competition and as a result recorded an album . The album received great reviews. Morgunbladid gave them 4,5 /5 stars and the album was played and reviewed very favourably in the Icelandic National Radio's show Fimm fjordu (5/4).

In February 2009 they took part in the Scandanavian Concert Series, Winter Jazz. (Nasjonal Jazzscene Oslo, Rytmihäiriöklubi Helsinki, Christianshavns Beboerhus Copenhagen, Mariehamn Jazzfestival in Åland Islands og Ylläs Jazz and blues in Lappland) In April 2009 the trio was chosen to take part in the EBU European Jazz Competition finals which is part of the North Sea Jazz Festival.

12 july 2010 the trio released there second album Rekaviður(driftwood) on the label Dimma (‬www.dimma.is‪). The album got outstanding reviews in Icelandic media. The trio toured extensively in Iceland to introduce the new CD Rekaviður.
At this time the trio played with Andri Ólafsson Double Bass player.

Kristján Martinsson the founder and main composer of K trio is now living in Amsterdam, Netherlands for further piano and composition studies at the Concervatorium van Amsterdam.
In Amsterdam the trio became truly multi national when Icelandic Kristján Martinsson started playing with British bass player Pat Cleaver and Latvian drummer Andris Buikis.
K trio has for the last year been performing in Amsterdam and the surrounding area. On 29th March 2012 the trio played in the 'Keep an eye Jazz Award 2012' semi-finals. The trio's repertoire, composed mostly by Kristján, combines the virtuosity of jazz, emotion of rock and pure joy.
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