  In this paper, an overview is presented of the recent construction of fully
back-reacted half-BPS solutions in 11-dimensional supergravity which correspond
to near-horizon geometries of M2 branes ending on, or intersecting with, M5 and
M5$'$ branes along a self-dual string. These solutions have space-time manifold
${\rm AdS}_3 \times S^3 \times S^3$ warped over a Riemann surface $\Sigma$, and
are invariant under the exceptional Lie superalgebra $D(2,1;\gamma) \oplus
D(2,1;\gamma)$, where $\gamma $ is a real continuous parameter and $|\gamma|$
is governed by the ratio of the number of M5 and M5$'$ branes. The construction
proceeds by mapping the reduced BPS equations onto an integrable field theory
on $\Sigma$ which is of the Liouville sine-Gordon type. Families of regular
solutions are distinguished by the sign of $\gamma$, and include a
two-parameter Janus solution for $\gamma >0$, and self-dual strings on M5 as
well as asymptotically ${\rm AdS}_4/{\mathbb Z}_2$ solutions for $\gamma <0$.
