Mixture models are central to panel data analysis. In this talk I study the ability of parametric and nonparametric mixture methods to identify and estimate nonlinear relationships on longitudinal data. Discrete and continuous mixtures have different strengths and weaknesses. I study their properties in panels of fixed lengths as the size of the cross-section increases, and in an alternative asymptotic where the number of units and time periods tend to infinity jointly. I discuss applications to the estimation of dynamic structural economic models with unobserved heterogeneity, and to the analysis of treatment effects in panel data studies.