In this paper, we present a compositional and dynamic model for face aging. The compositional model represents faces in each age group by a hierarchical And-or graph, in which And nodes decompose a face into parts to describe details (e.g., hair, wrinkles, etc.) crucial for age perception and Or nodes represent large diversity of faces by alternative selections. Then a face instance is a transverse of the And-or graph-parse graph. Face aging is modeled as a Markov process on the parse graph representation. We learn the parameters of the dynamic model from a large annotated face data set and the stochasticity of face aging is modeled in the dynamics explicitly. Based on this model, we propose a face aging simulation and prediction algorithm. Inversely, an automatic age estimation algorithm is also developed under this representation. We study two criteria to evaluate the aging results using human perception experiments: (1) the accuracy of simulation: whether the aged faces are perceived of the intended age group, and (2) preservation of identity: whether the aged faces are perceived as the same person. Quantitative statistical analysis validates the performance of our aging model and age estimation algorithm.