The cubic complex Ginzburg-Landau equation (CGLe) is a widely studied nonlinear equation in physics, describing a broad range of phenomena from nonlinear waves to phase transitions, superconductivity, superfluidity, and liquid crystals. This review provides an overview of the CGLe's behavior in one, two, and three dimensions from the perspective of condensed matter physicists. The focus is on understanding nonequilibrium phenomena in spatially extended systems through the study of relevant solutions. The CGLe is derived from a generalization of the Ginzburg-Landau equation, incorporating both linear and nonlinear dispersion. It is used to describe weakly nonlinear spatio-temporal phenomena in systems with general linear dispersion and global gauge invariance. The equation is valid under conditions such as the correct choice of order parameter space, the validity of the dispersion relation, symmetry considerations, and the weakly nonlinear approximation. The CGLe can be classified into three primary bifurcation types: stationary periodic instabilities, oscillatory uniform instabilities, and oscillatory periodic instabilities. Each type has distinct characteristics and applications in various physical systems, including fluid dynamics, chemical reactions, and optical systems. The equation exhibits a wide range of phenomena, including coherent structures, phase and defect turbulence, spatio-temporal chaos, and vortex dynamics. In one dimension, the CGLe describes sink and source solutions, vortex dynamics, and spatio-temporal chaos. In two dimensions, it describes spiral stability, vortex dynamics, and defect chaos. In three dimensions, it describes vortex line motion, vortex ring collapse, and vortex nucleation and reconnection. The CGLe has been generalized to include various forms, such as subcritical CGLe, complex Swift-Hohenberg equation, and anisotropic CGLe. These generalizations allow for a broader understanding of the equation's behavior in different physical contexts. The CGLe is a powerful tool for studying nonlinear phenomena in spatially extended systems, providing insights into the behavior of complex systems ranging from superconductivity to liquid crystals. Its applications span across various fields, making it a fundamental equation in the study of nonlinear dynamics and pattern formation.The cubic complex Ginzburg-Landau equation (CGLe) is a widely studied nonlinear equation in physics, describing a broad range of phenomena from nonlinear waves to phase transitions, superconductivity, superfluidity, and liquid crystals. This review provides an overview of the CGLe's behavior in one, two, and three dimensions from the perspective of condensed matter physicists. The focus is on understanding nonequilibrium phenomena in spatially extended systems through the study of relevant solutions. The CGLe is derived from a generalization of the Ginzburg-Landau equation, incorporating both linear and nonlinear dispersion. It is used to describe weakly nonlinear spatio-temporal phenomena in systems with general linear dispersion and global gauge invariance. The equation is valid under conditions such as the correct choice of order parameter space, the validity of the dispersion relation, symmetry considerations, and the weakly nonlinear approximation. The CGLe can be classified into three primary bifurcation types: stationary periodic instabilities, oscillatory uniform instabilities, and oscillatory periodic instabilities. Each type has distinct characteristics and applications in various physical systems, including fluid dynamics, chemical reactions, and optical systems. The equation exhibits a wide range of phenomena, including coherent structures, phase and defect turbulence, spatio-temporal chaos, and vortex dynamics. In one dimension, the CGLe describes sink and source solutions, vortex dynamics, and spatio-temporal chaos. In two dimensions, it describes spiral stability, vortex dynamics, and defect chaos. In three dimensions, it describes vortex line motion, vortex ring collapse, and vortex nucleation and reconnection. The CGLe has been generalized to include various forms, such as subcritical CGLe, complex Swift-Hohenberg equation, and anisotropic CGLe. These generalizations allow for a broader understanding of the equation's behavior in different physical contexts. The CGLe is a powerful tool for studying nonlinear phenomena in spatially extended systems, providing insights into the behavior of complex systems ranging from superconductivity to liquid crystals. Its applications span across various fields, making it a fundamental equation in the study of nonlinear dynamics and pattern formation.