Two-dimensional conformal field theory (CFT) on open and unoriented surfaces is not a recent discovery. Its systematic study began in two seemingly different developments. On the one hand, the implications of the presence of a boundary in two-dimensional systems and the corresponding boundary conditions and boundary fields were first analysed by J.L. Cardy. On the other hand, a general prescription for the systematic construction of open and unoriented string models from a given closed oriented string model was proposed by A. Sagnotti. This chapter reviews some general properties of two-dimensional CFT and derives explicit expressions for the 4-point functions in the SU (2) Wess-Zumino-Witten model, the corresponding exchange operators and fusion matrix. It discusses the sewing constraints for the correlation functions on open and unoriented surfaces and analyses the partition functions and the consistency conditions they satisfy.