With his eponymous group, Haftor has recorded five albums and subsequently released albums with Will of the People (Pete Furniss - clarinet and Tom Bancroft - drums), Jacob Karlzon (piano), Espen Eriksen (piano) and Gunnar Halle (trumpet), Anneke Kampman (ex Conquering Animal Sound, ANAKANAK).

As a composer, Haftor has scored music for numerous film and television productions including Building a Nation (Wark Clemmens for C4) and the multi award-winning Tartan Short, Cry For Bobo (David Cairns). Other composition credits include the 2014 son et lumiere production, A Night at The Botanics, collaborative installation pieces with artists Alan Kilpatrick and Michele Marcoux, dance/video productions by choreographer/film-maker Katrina MacPherson and commissioned responses to a number of exhibitions for the National Galleries of Scotland.

Haftor is Professor of Music at Edinburgh Napier University, where he gained his doctoral degree in 2013. He is an internationally published  researcher in the field of new jazz studies and has presented conference papers throughout Europe for, amongst others, the International Society of Musicologists, Rhythm Changes, KISMIF, HEA and the Nordic Research Network. Haftor is founding Chair of the Scottish Jazz Archive and a Director of the Edinburgh Jazz & Blues Festival.

Haftor Medbøe is a Yamaha artist