This paper provides a comprehensive review of econometric methods for dynamic panel data models, focusing on single equation models with autoregressive dynamics and non-strictly exogenous explanatory variables. The emphasis is on Generalized Method of Moments (GMM) estimators, which are widely used in this context. The paper discusses two main types of models: simple autoregressive models and multivariate dynamic models with persistent series. For simple autoregressive models, the paper details the estimation methods, including the Within Groups estimator, First-Differenced Two Stage Least Squares (2SLS), and GMM estimators. It highlights the importance of predetermined initial conditions and the use of instrumental variables. The paper also discusses the validity of these estimators under different assumptions about the initial conditions and the serial correlation in the disturbances. For multivariate dynamic models, the paper extends the GMM estimators to include autoregressive-distributed lag models. It explores the conditions under which additional moment conditions can be used, such as when the explanatory variables are correlated with the error term but uncorrelated with the individual effects. The paper also addresses the issue of persistent series, where lagged levels of the series may be invalid instruments, and the potential for finite sample biases in instrumental variable estimators. The paper concludes with a discussion of the practical implications of these methods, emphasizing the importance of considering the time series properties of the data and the validity of additional moment conditions when dealing with highly persistent series.This paper provides a comprehensive review of econometric methods for dynamic panel data models, focusing on single equation models with autoregressive dynamics and non-strictly exogenous explanatory variables. The emphasis is on Generalized Method of Moments (GMM) estimators, which are widely used in this context. The paper discusses two main types of models: simple autoregressive models and multivariate dynamic models with persistent series. For simple autoregressive models, the paper details the estimation methods, including the Within Groups estimator, First-Differenced Two Stage Least Squares (2SLS), and GMM estimators. It highlights the importance of predetermined initial conditions and the use of instrumental variables. The paper also discusses the validity of these estimators under different assumptions about the initial conditions and the serial correlation in the disturbances. For multivariate dynamic models, the paper extends the GMM estimators to include autoregressive-distributed lag models. It explores the conditions under which additional moment conditions can be used, such as when the explanatory variables are correlated with the error term but uncorrelated with the individual effects. The paper also addresses the issue of persistent series, where lagged levels of the series may be invalid instruments, and the potential for finite sample biases in instrumental variable estimators. The paper concludes with a discussion of the practical implications of these methods, emphasizing the importance of considering the time series properties of the data and the validity of additional moment conditions when dealing with highly persistent series.