Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal laws in turbulence and finance in relation to temporal processes (iii) Stochastic integration for time changed volatility modulated Levy-driven Volterra processes.

Keywords: ambit stochastics, extended subordination, finance, metatimes, non-semimartingales, stochastic integration, time-change, stochastic volatility/intermittency, turbulence, universality.