The 1997 review of modelling and image reconstruction techniques (Arridge and Hebden 1997) is still a useful introduction to the basic theoretical concepts. Progress since 1997 has largely focussed on developing more realistic and efficient models of light transport in tissue, and on solving the ill-posed inverse problem in an increasingly rigorous way. In particular, it is becoming increasingly common to include prior information of the anatomy and optical properties of tissue in both the modelling and the image reconstruction.