Inhomogeneous Markov processes

We present the foundations of the theory of nonhomogeneous Markov processes in general state spaces and we give a survey of the fundamental papers in this topic. We consider the following questions:
1. The existence of transition functions for a Markov process.
2. The construction of regularization of processes.
3. The properties of right and left processes: the strict Markov property, the behavior of excessive functions, etc.
4. The relation of right and left processes with dual homogeneous processes and the application of the results of the nonhomogeneous theory to dual homogeneous processes, etc.