This review discusses spatiotemporal pattern formation in systems driven away from equilibrium, focusing on comparisons between theory and experiments. Examples include patterns in hydrodynamic systems like thermal convection, Taylor-Couette flow, and parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions, and excitable biological media. Theoretical methods start with deterministic equations of motion, often nonlinear partial differential equations, and may include stochastic terms. The aim is to describe solutions that are likely to be reached from typical initial conditions and persist over time. A unified description is based on linear instabilities of a homogeneous state, leading to classification of patterns by characteristic wave vector $ q_0 $ and frequency $ \omega_0 $. Type $ I_s $ systems are stationary and periodic in space, type $ III_0 $ systems are periodic in time and uniform in space, and type $ I_0 $ systems are periodic in both. Near a continuous instability, dynamics are described by amplitude equations, which are universal for each instability type. Far from the instability threshold, a phase equation may be used, but it is restricted to slow distortions of an ideal pattern. Phenomenological order-parameter models are useful for deriving amplitude equations and analyzing nonlinear regimes. Theoretical methods are applied to analyze real pattern effects like boundary influences and defect dynamics. Deterministic chaos is a key feature of nonequilibrium systems, with different analyses for systems with few and many degrees of freedom. The review includes detailed discussions of various systems, such as Rayleigh-Bénard convection, binary-fluid convection, electrohydrodynamic convection, Taylor-Couette flow, parametric surface waves, and others. It also addresses pattern selection, defects, and spatiotemporal chaos, as well as the challenges in understanding these phenomena. The review concludes with an assessment of what has been accomplished and what remains to be done in the field.This review discusses spatiotemporal pattern formation in systems driven away from equilibrium, focusing on comparisons between theory and experiments. Examples include patterns in hydrodynamic systems like thermal convection, Taylor-Couette flow, and parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions, and excitable biological media. Theoretical methods start with deterministic equations of motion, often nonlinear partial differential equations, and may include stochastic terms. The aim is to describe solutions that are likely to be reached from typical initial conditions and persist over time. A unified description is based on linear instabilities of a homogeneous state, leading to classification of patterns by characteristic wave vector $ q_0 $ and frequency $ \omega_0 $. Type $ I_s $ systems are stationary and periodic in space, type $ III_0 $ systems are periodic in time and uniform in space, and type $ I_0 $ systems are periodic in both. Near a continuous instability, dynamics are described by amplitude equations, which are universal for each instability type. Far from the instability threshold, a phase equation may be used, but it is restricted to slow distortions of an ideal pattern. Phenomenological order-parameter models are useful for deriving amplitude equations and analyzing nonlinear regimes. Theoretical methods are applied to analyze real pattern effects like boundary influences and defect dynamics. Deterministic chaos is a key feature of nonequilibrium systems, with different analyses for systems with few and many degrees of freedom. The review includes detailed discussions of various systems, such as Rayleigh-Bénard convection, binary-fluid convection, electrohydrodynamic convection, Taylor-Couette flow, parametric surface waves, and others. It also addresses pattern selection, defects, and spatiotemporal chaos, as well as the challenges in understanding these phenomena. The review concludes with an assessment of what has been accomplished and what remains to be done in the field.