  In this paper we present a survey on recent developments in the study of
ambit fields and point out some open problems. Ambit fields is a class of
spatio-temporal stochastic processes, which by its general structure
constitutes a flexible model for dynamical structures in time and/or in space.
We will review their basic probabilistic properties, main stochastic
integration concepts and recent limit theory for high frequency statistics of
ambit fields.
