  Continuous Time Random Walks (CTRWs) are jump processes with random waiting
times between jumps. We study scaling limits for CTRWs where the distribution
of jumps and waiting times is coupled and varies in space and time. Such
processes model e.g. anomalous diffusion processes in a space- and
time-dependent potential. Conditions for the process-convergence of CTRWs are
given, and the limits are characterised by four coefficients. Kolmogorov
forwards and backwards equations with non-local time operators are derived, and
three models for anomalous diffusion are presented: i) Subdiffusion in a
time-dependent potential, ii) subdiffusion with spatially varying waiting times
and iii) L\'evy walks with space- and time-dependent drift.
