We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous‐agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence‐space Jacobians—the derivatives of perfect‐foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous‐agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood‐based estimation and computation of nonlinear perfect‐foresight transitions. We apply our methods to three canonical heterogeneous‐agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.