The And-Or graph is a tool for knowledge representation. In this thesis we first study the sampling of the And-Or graph with or without context constraints. Without any constraint on the potential functions of the And-Or graph nodes, the positions and shapes of different components of the face images are not aligned properly. In contrast, with both unary constraints and binary constraints, the components are aligned and the samples are more representative of the And-Or graph. We further explore parameter and structure learning of the And-Or graph by implementing and applying some existing algorithms. The experimental results on 1D text data and 2D face image data are shown. While there is no apparent difference between the sampling results of the parameter learned And-Or graph and the true And-Or graph, the sampling results of the structure learned And-Or graph are not perfect and could be further improved.