  The main purpose of this paper is to discuss Hardy type spaces, Bloch type
spaces and the composition operators of complex-valued harmonic functions. We
first establish a sharp estimate of the Lipschitz continuity of complex-valued
harmonic functions in Bloch type spaces with respect to the pseudo-hyperbolic
metric, which gives an answer to an open problem. Then some classes of
composition operators on Bloch and Hardy type spaces will be investigated. The
obtained results improve and extend some corresponding known results.
