  This article is devoted to the study of the critical properties of classical
XY and Heisenberg frustrated magnets in three dimensions. We first analyze the
experimental and numerical situations. We show that the unusual behaviors
encountered in these systems, typically nonuniversal scaling, are hardly
compatible with the hypothesis of a second order phase transition. We then
review the various perturbative and early nonperturbative approaches used to
investigate these systems. We argue that none of them provides a completely
satisfactory description of the three-dimensional critical behavior. We then
recall the principles of the nonperturbative approach - the effective average
action method - that we have used to investigate the physics of frustrated
magnets. First, we recall the treatment of the unfrustrated - O(N) - case with
this method. This allows to introduce its technical aspects. Then, we show how
this method unables to clarify most of the problems encountered in the previous
theoretical descriptions of frustrated magnets. Firstly, we get an explanation
of the long-standing mismatch between different perturbative approaches which
consists in a nonperturbative mechanism of annihilation of fixed points between
two and three dimensions. Secondly, we get a coherent picture of the physics of
frustrated magnets in qualitative and (semi-) quantitative agreement with the
numerical and experimental results. The central feature that emerges from our
approach is the existence of scaling behaviors without fixed or pseudo-fixed
point and that relies on a slowing-down of the renormalization group flow in a
whole region in the coupling constants space. This phenomenon allows to explain
the occurence of generic weak first order behaviors and to understand the
absence of universality in the critical behavior of frustrated magnets.
