The goal of this paper is threefold. First, we survey the existing results on Hunt's hypothesis (H) for Markov processes and Getoor's conjecture for L\'{e}vy processes. Second, we investigate (H) for multidimensional L\'{e}vy processes from the viewpoint of projections. Third, we present a few open questions for further study. The talk is based on a joint work with Wei Sun (Concordia University).