We present some results from approximation theory of fuzzy-number-valued functions. These functions could play an important role in modelling fuzzy dynamical systems, i.e. dynamical systems under uncertainty. Results on fuzzy (trigonometric) polynomial approximation are presented, Jackson-type estimates and existence of best approximation polynomials is discussed. Possible extension of this theory to fuzzy-number-valued functions having their range in fuzzy number's space and applications to fuzzy control are outlined.