  We review results concerning the critical behavior of spin systems at
equilibrium. We consider the Ising and the general O($N$)-symmetric
universality classes, including the $N\to 0$ limit that describes the critical
behavior of self-avoiding walks. For each of them, we review the estimates of
the critical exponents, of the equation of state, of several amplitude ratios,
and of the two-point function of the order parameter. We report results in
three and two dimensions. We discuss the crossover phenomena that are observed
in this class of systems. In particular, we review the field-theoretical and
numerical studies of systems with medium-range interactions. Moreover, we
consider several examples of magnetic and structural phase transitions, which
are described by more complex Landau-Ginzburg-Wilson Hamiltonians, such as
$N$-component systems with cubic anisotropy, O($N$)-symmetric systems in the
presence of quenched disorder, frustrated spin systems with noncollinear or
canted order, and finally, a class of systems described by the tetragonal
Landau-Ginzburg-Wilson Hamiltonian with three quartic couplings. The results
for the tetragonal Hamiltonian are original, in particular we present the
six-loop perturbative series for the $\beta$-functions. Finally, we consider a
Hamiltonian with symmetry $O(n_1)\oplus O(n_2)$ that is relevant for the
description of multicritical phenomena.
