  We review the recent approach to the construction of (3+1)-dimensional
integrable dispersionless partial differential systems based on their contact
Lax pairs and the related $R$-matrix theory for the Lie algebra of functions
with respect to the contact bracket. We discuss various kinds of Lax
representations for such systems, in particular, linear nonisospectral contact
Lax pairs and nonlinear contact Lax pairs as well as the relations among the
two. Finally, we present a large number of examples with finite and infinite
number of dependent variables, as well as the reductions of these examples to
lower-dimensional integrable dispersionless systems.
