The cubic complex Ginzburg-Landau (CGLe) equation is a widely studied nonlinear equation in physics, describing a broad range of phenomena from nonlinear waves to phase transitions, superconductivity, superfluidity, Bose-Einstein condensation, liquid crystals, and field theory. This chapter provides an overview of the CGLe from the perspective of condensed matter physicists, focusing on its solutions to gain insights into nonequilibrium phenomena in spatially extended systems. The CGLe is given by the equation: \[ \partial_t A = A + (1 + ib)\Delta A - (1 + ic)|A|^2 A, \] where \(A\) is a complex function of time and space, and \(b\) and \(c\) are real parameters characterizing linear and nonlinear dispersion. The equation arises as a "modulational" or "envelope" equation, providing a reduced description of weakly nonlinear spatio-temporal phenomena in extended media with general linear dispersion and global gauge invariance. The chapter covers various aspects of the CGLe, including: - **Preliminary Remarks**: Introduction to the equation, its historical context, and its applications. - **General Considerations**: Variational case, amplitude-phase representation, transformations, coherent structures, similarity, plane-wave solutions, and their stability. - **Dynamics in 1D**: Classification of coherent structures, sinks and sources, Nozaki-Bekki hole solutions, other coherent structures, spatio-temporal chaos, and phase equations. - **Dynamics in 2D**: Spiral stability, dynamics of vortices, interactions of spirals with inhomogeneities, symmetry breaking, and vortex glass. - **Dynamics in 3D**: Vortex line motion, collapse of vortex rings, vortex nucleation, and reconnection. - **Generalizations of the CGLe**: Subcritical CGLe, complex Swift-Hohenberg equation, CGLe with broken gauge invariance, anisotropic CGLe, coupled Ginzburg-Landau equations, complex defects in vector Ginzburg-Landau equation, and complex oscillatory media. The chapter also discusses the historical development of the CGLe, key concepts, and the validity conditions for the equation. It highlights the importance of the CGLe in understanding various physical phenomena and its role in pattern-forming systems and nonlinear wave dynamics.The cubic complex Ginzburg-Landau (CGLe) equation is a widely studied nonlinear equation in physics, describing a broad range of phenomena from nonlinear waves to phase transitions, superconductivity, superfluidity, Bose-Einstein condensation, liquid crystals, and field theory. This chapter provides an overview of the CGLe from the perspective of condensed matter physicists, focusing on its solutions to gain insights into nonequilibrium phenomena in spatially extended systems. The CGLe is given by the equation: \[ \partial_t A = A + (1 + ib)\Delta A - (1 + ic)|A|^2 A, \] where \(A\) is a complex function of time and space, and \(b\) and \(c\) are real parameters characterizing linear and nonlinear dispersion. The equation arises as a "modulational" or "envelope" equation, providing a reduced description of weakly nonlinear spatio-temporal phenomena in extended media with general linear dispersion and global gauge invariance. The chapter covers various aspects of the CGLe, including: - **Preliminary Remarks**: Introduction to the equation, its historical context, and its applications. - **General Considerations**: Variational case, amplitude-phase representation, transformations, coherent structures, similarity, plane-wave solutions, and their stability. - **Dynamics in 1D**: Classification of coherent structures, sinks and sources, Nozaki-Bekki hole solutions, other coherent structures, spatio-temporal chaos, and phase equations. - **Dynamics in 2D**: Spiral stability, dynamics of vortices, interactions of spirals with inhomogeneities, symmetry breaking, and vortex glass. - **Dynamics in 3D**: Vortex line motion, collapse of vortex rings, vortex nucleation, and reconnection. - **Generalizations of the CGLe**: Subcritical CGLe, complex Swift-Hohenberg equation, CGLe with broken gauge invariance, anisotropic CGLe, coupled Ginzburg-Landau equations, complex defects in vector Ginzburg-Landau equation, and complex oscillatory media. The chapter also discusses the historical development of the CGLe, key concepts, and the validity conditions for the equation. It highlights the importance of the CGLe in understanding various physical phenomena and its role in pattern-forming systems and nonlinear wave dynamics.