Abstract: This paper gives an overview of different measures of complexity proposed to characterize dynamical systems developed during recent years. The emphasis is placed on the distinction of complexity from randomness. Those measures, which were used to characterize chaos, including Lyapunov exponent,topologic al entropy, metric entropy, Kolmogorov complexity etc., are reviewed briefly in this sense. New measures, including AC, SC, EMC among others,are explained from the point of view of both automata and informat...