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 and composition of sequence-space Jacobians—the derivatives of perfect-foresight equilibrium mappings between aggregate sequences around the steady state. We provide a fast algorithm for computing Jacobians for heterogeneous agents, a technique to substantially reduce dimensionality, a rapid procedure for likelihood-based estimation, a determinacy condition for the sequence space, and a method to solve 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.