Summary: Based on the first hitting time or return time, we review the development of Markov chain in the study of stationarity, quasi-stationarity and asymmetry. These topics include: (1) using the moments of the return time to derive the functional inequalities; (2) introducing the modified return time to describe the various transience; (3) obtaining the functional inequalities via the return times; (4) using the eigenvalues to describe the distribution of the hitting times; (5) giving the criteria for the cut-off by the hitting times; (6) obtaining the quasi-stationary distribution through the distribution of the life times; (7) developing the Dirichlet principle to judge which is better between the non-reversible Markov chain and its reversible one.