A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in various wavenumber ranges, which depend on the anisotropy of the dielectric permittivity and that of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). We discuss in detail three basic configurations with emphasis on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. Some features of the weakly nonlinear behavior are also addressed. Experimental exploration of additional pattern types, not captured by the standard model of electroconvection, is also presented. The impact of flexoelectricity as a possible explanation of the nonstandard EC patterns is discussed.