  We find exact solutions of topologically massive gravity (TMG) and new
massive gravity (NMG) in ${2+1}$ dimensions (3D) with an arbitrary cosmological
constant, pure radiation, and gyratons, i.e., with possibly non-zero $T_{uu}$
and $T_{ux}$ in canonical coordinates. Since any `reasonable' geometry in 3D
(i.e., admitting a null geodesic congruence) is either expanding
Robinson-Trautman ($\Theta\neq 0$) or Kundt (${\Theta=0}$), we focus on these
two classes. Assuming expansions ${\Theta=1/r}$ (`GR-like' Robinson-Trautman)
or ${\Theta=0}$ (general Kundt), we systematically integrate the field
equations of TMG and NMG and identify new classes of exact solutions. The case
of NMG contains an additional assumption of $g_{ux}$ being quadratic in $r$,
which is automatically enforced in TMG as well as in 3D GR. In each case, we
reduce the field equations as much as possible and identify new classes of
solutions. We also discuss various special subclasses and study some explicit
solutions.
