  We review the definition of determinants for finite von Neumann algebras, due
to Fuglede and Kadison (1952), and a generalisation for appropriate groups of
invertible elements in Banach algebras, from a paper by Skandalis and the
author (1984). After some reminder on K-theory and Whitehead torsion, we hint
at the relevance of these determinants to the study of $L^2$-torsion in
topology.
