Markov Chains are an important class of stochastic processes that are widely used in practice to determine system performance and dependability characteristics. This talk will consider discrete-time and continuous-time Markov chains and explain notions of strong and weak simulation and bisimulation relations for them. Moreover, the talk will discuss the connection between the several types of branching relation, present decision algorithms and logical characterisations by PCTL (probabilistic computation tree logic) and CSL (continuous stochastic logic).