  We give the overview of solution techniques for the general
conformally-invariant linear and nonlinear wave equations centered around the
idea of dimensional reductions by their symmetry groups. The efficiency of
these techniques is demonstrated on the examples of the SU(2) Yang-Mills and
the vacuum Maxwell equations. For the Yang-Mills equations we have derived the
most general form of the conformally-invariant solution and construct a number
of their new analytical non-Abelian solutions in explicit form. We have
completely solved the problem of symmetry reduction of the Maxwell equations by
subgroups of the conformal group. This yields twelve multi-parameter families
of their exact solutions, a majority of which are new and might be of
considerable interest for applications.
