This chapter provides a comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium, emphasizing the comparison between theoretical models and quantitative experiments. The authors, M. C. Cross and P. C. Hohenberg, discuss various systems such as hydrodynamic systems (e.g., thermal convection, Taylor-Couette flow), solidification fronts, nonlinear optics, oscillatory chemical reactions, and excitable biological media. They focus on the theoretical aspects, starting with deterministic equations of motion, often in the form of nonlinear partial differential equations, and sometimes supplemented by stochastic terms. The aim is to describe solutions that are likely to be reached from typical initial conditions and persist over long times. The theoretical framework is based on linear instabilities of a homogeneous state, leading to a classification of patterns into types I, II, and III based on the characteristic wave vector and frequency of the instability. The chapter also covers the development of amplitude equations and phase equations, as well as the use of phenomenological order-parameter models. It discusses the role of boundaries and defects in real patterns, the dynamics of defects, and pattern selection mechanisms. Additionally, it explores chaotic states in nonequilibrium systems and the theoretical methods used to analyze them, including perturbation theory, qualitative methods, and numerical simulations. The chapter concludes with a summary of what has been accomplished and what remains to be done in the field, along with future prospects.This chapter provides a comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium, emphasizing the comparison between theoretical models and quantitative experiments. The authors, M. C. Cross and P. C. Hohenberg, discuss various systems such as hydrodynamic systems (e.g., thermal convection, Taylor-Couette flow), solidification fronts, nonlinear optics, oscillatory chemical reactions, and excitable biological media. They focus on the theoretical aspects, starting with deterministic equations of motion, often in the form of nonlinear partial differential equations, and sometimes supplemented by stochastic terms. The aim is to describe solutions that are likely to be reached from typical initial conditions and persist over long times. The theoretical framework is based on linear instabilities of a homogeneous state, leading to a classification of patterns into types I, II, and III based on the characteristic wave vector and frequency of the instability. The chapter also covers the development of amplitude equations and phase equations, as well as the use of phenomenological order-parameter models. It discusses the role of boundaries and defects in real patterns, the dynamics of defects, and pattern selection mechanisms. Additionally, it explores chaotic states in nonequilibrium systems and the theoretical methods used to analyze them, including perturbation theory, qualitative methods, and numerical simulations. The chapter concludes with a summary of what has been accomplished and what remains to be done in the field, along with future prospects.