Markov state models (MSMs) approximate the long-time statistical dynamics of a molecule using a Markov chain on a discrete partition of configuration space. These models are widely used in molecular dynamics simulations to analyze kinetic behavior, as they allow for the extraction of long-time kinetic information from short trajectories and enable the calculation of expectation values and statistical uncertainties of various molecular observables. This paper summarizes the current state of the art in generating and validating MSMs, highlighting key results and insights. The paper discusses the approximation error introduced by modeling molecular dynamics with an MSM, showing that this error can be made arbitrarily small with minimal effort. It emphasizes that the best MSM is not obtained by the most metastable discretization, but by introducing non-metastable states near transition states. Additionally, it shows that it is not necessary to resolve all slow processes by state space partitioning, as individual dynamical processes of interest can be resolved separately. The paper also presents an efficient estimator for reversible transition matrices and a robust test to validate that an MSM reproduces the kinetics of molecular dynamics data. It discusses the essential properties of the true continuous dynamics and how they may be affected by simulation details. It examines the effect of discretizing the state space to produce a discrete-state Markov chain approximation and provides a detailed analysis of the error incurred in this process. The paper also introduces the transfer operator approach and the dominant spectrum, explaining how the dynamics can be decomposed into a superposition of slow and fast processes. It discusses the implications of discretization error and non-Markovianity, emphasizing the importance of choosing appropriate discretization and lag times to minimize approximation errors. The paper concludes that MSMs can accurately model long-time kinetics despite being constructed from short trajectories, and that the statistical uncertainty of the model can be used to adaptively guide model construction.Markov state models (MSMs) approximate the long-time statistical dynamics of a molecule using a Markov chain on a discrete partition of configuration space. These models are widely used in molecular dynamics simulations to analyze kinetic behavior, as they allow for the extraction of long-time kinetic information from short trajectories and enable the calculation of expectation values and statistical uncertainties of various molecular observables. This paper summarizes the current state of the art in generating and validating MSMs, highlighting key results and insights. The paper discusses the approximation error introduced by modeling molecular dynamics with an MSM, showing that this error can be made arbitrarily small with minimal effort. It emphasizes that the best MSM is not obtained by the most metastable discretization, but by introducing non-metastable states near transition states. Additionally, it shows that it is not necessary to resolve all slow processes by state space partitioning, as individual dynamical processes of interest can be resolved separately. The paper also presents an efficient estimator for reversible transition matrices and a robust test to validate that an MSM reproduces the kinetics of molecular dynamics data. It discusses the essential properties of the true continuous dynamics and how they may be affected by simulation details. It examines the effect of discretizing the state space to produce a discrete-state Markov chain approximation and provides a detailed analysis of the error incurred in this process. The paper also introduces the transfer operator approach and the dominant spectrum, explaining how the dynamics can be decomposed into a superposition of slow and fast processes. It discusses the implications of discretization error and non-Markovianity, emphasizing the importance of choosing appropriate discretization and lag times to minimize approximation errors. The paper concludes that MSMs can accurately model long-time kinetics despite being constructed from short trajectories, and that the statistical uncertainty of the model can be used to adaptively guide model construction.