  Low-rank matrix recovery problems are inverse problems which naturally arise
in various fields like signal processing, imaging and machine learning. They
are non-convex and NP-hard in full generality. It is therefore a delicate
problem to design efficient recovery algorithms and to provide rigorous
theoretical insights on the behavior of these algorithms. The goal of these
notes is to review recent progress in this direction for the class of so-called
"non-convex algorithms", with a particular focus on the proof techniques.
  Although they aim at presenting very recent research works, these notes have
been written with the intent to be, as much as possible, accessible to
non-specialists.
