The study of the combinatorial properties of convex polyhedra is equivalent to the study of the properties of graphs determined by vertices and edges of convex three-dimensional polytopes. This book presents a review of both well-known and new findings on polyhedral graphs. Each chapter provides open problems and addresses an essential topic in the field. These topics include face and edge types, light edges and paths, connected subgraphs with restricted degrees of vertices, spanning subgraphs, cycles in polyhedral graphs, face-vectors and vertex-vectors of complex polyhedra, groups of symmetries, duality in polyhedra, and the coloring of polyhedral graphs.