abstract: Interval translation mappings (ITMs) were introduced by M. Boshernitzan and I. Kornfeld in 90s as a natural generalisation of interval exchange transformations (IETs). As in case of IETs, we deal with the piecewise continuous map defined on the interval, on each interval of continuity the map is a shift. However, the images of different intervals in case of ITMs can overlap. In my talk I will discuss different approaches to study dynamical properties of ITMs, from complexity to ergodicity and weak mixing. The talk is partly based on joint works with M. Artigiani, P. Hubert and Ch. Fougeron.