This volume consists ofsurvey articles on current topics in computational wave prop agation and inverse problems, written by leading experts in their respective fields. The idea to compile such a volume arose in conjunction with the LMS Durham Symposium on Computational Methods for Wave Propagation in Direct Scattering held at the University of Durham from 15th-25th July 2002, which we jointly or ganised. The meeting, attended by 70 participants from the UK and overseas, was structured around a number of short, three lecture, survey courses on a range of top ics on computational wave...