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Probabilistic programs extend classical imperative programs with random-value generators. For classical non-probabilistic programs, termination is a key question in static analysis of programs, that given a program and an initial condition asks whether it terminates. In the presence of probabilistic behavior there are two fundamental extensions of the termination question, namely,(a) the almostsure termination question that asks whether the termination probability is 1; and (b) the bounded-time termination question that asks whether the expected termination time is bounded. While there are many active research directions to address the above problems, one important research direction is the use of martingale theory for termination analysis. We will survey the main techniques related to martingale-based approach for termination analysis of probabilistic programs.