This paper presents results on steady-state analysis and regulation for nonlinear discrete-time systems subject to time-varying excitations. In the analysis part of the paper, for convergent nonlinear systems (which have uniquely defined steady-state responses to excitations) we provide a complete characterization of the steady-state responses to excitations generated by an exosystem. As a corollary, we obtain a nonlinear frequency response function which extends the well-known FRF defined for linear systems to the class of nonlinear convergent systems. In the control part of the paper, we present a characterization of all controllers solving the global output regulation problem. All these results are obtained using the machinery of convergent systems, extended to the discrete-time setting. For piecewise affine systems, general results are supplied with a constructive design procedure.