  We study the nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the fundamental and adjoint representation. Universality
and renormalization-group (RG) arguments show that the possibility of having a
continuous transition is related to the existence of a stable fixed point (FP)
in the RG flow of a 3D Landau-Ginzburg-Wilson Phi^4 theory with the same chiral
symmetry-breaking pattern. The RG flow of these theories is studied by
field-theoretical approaches, computing and analyzing high-order perturbative
series, up to six loops. According to this RG analysis, the transition in QCD
can be continuous only for N_f=2. In this case it belongs to the 3D O(4)
universality class. We also find a stable FP corresponding to a 3D universality
class with symmetry breaking U(2)_L x U(2)_R -> U(2)_V, which implies that the
transition can be continuous also if the axial-anomaly effects are suppressed
at Tc. In the case of quarks in the adjoint representation, we can have a
continuous transition for N_f=1,2. For N_f=1 it belongs to the O(3)
universality class. For N_f=2 it belongs to a new 3D universality class
characterized by the symmetry breaking SU(4)->SO(4).
