The talk will focus on algorithms for the computation of the steady-state response of nonlinear circuits excited by periodic and quasi-periodic signals. We first formulate the periodic steady-state problem in time and frequency domains, and describe the method of harmonic-balance, a frequency-domain algorithm. The harmonic-balance algorithm is rendered efficient and practical for large circuits by use of preconditioned, Krylov subspace-based iterative methods for solving the large and dense systems of linear equations which arise. Next, we address the computation of the quasi-periodic steady-state solution of circuits excited by several periodic stimuli of incommensurate frequencies. Here, we discuss a general formulation of the problem, from which we derive the frequency-domain solution method: multitone harmonic balance, and the mixed time-and-frequency domain method: envelope following. Again, these methods rely on the Krylov subspace-based iterative linear solvers.