This review provides a comprehensive overview of the critical behavior of spin systems at equilibrium, focusing on the Ising and O(N)-symmetric universality classes, including the N → 0 limit for self-avoiding walks. It covers critical exponents, the equation of state, amplitude ratios, and the two-point function of the order parameter for these systems in three and two dimensions. The authors discuss crossover phenomena, particularly in systems with medium-range interactions, and present field-theoretical and numerical studies. The review also explores more complex Landau-Ginzburg-Wilson Hamiltonians, such as N-component systems with cubic anisotropy, systems with quenched disorder, frustrated spin systems, and systems described by the tetragonal Landau-Ginzburg-Wilson Hamiltonian. Original results, including six-loop perturbative series for β-functions, are presented. The review concludes with a discussion of multicritical phenomena in systems with symmetry O(n1)⊕O(n2).This review provides a comprehensive overview of the critical behavior of spin systems at equilibrium, focusing on the Ising and O(N)-symmetric universality classes, including the N → 0 limit for self-avoiding walks. It covers critical exponents, the equation of state, amplitude ratios, and the two-point function of the order parameter for these systems in three and two dimensions. The authors discuss crossover phenomena, particularly in systems with medium-range interactions, and present field-theoretical and numerical studies. The review also explores more complex Landau-Ginzburg-Wilson Hamiltonians, such as N-component systems with cubic anisotropy, systems with quenched disorder, frustrated spin systems, and systems described by the tetragonal Landau-Ginzburg-Wilson Hamiltonian. Original results, including six-loop perturbative series for β-functions, are presented. The review concludes with a discussion of multicritical phenomena in systems with symmetry O(n1)⊕O(n2).