keV sterile neutrino Dark Matter

We give an overview of the current status of keV sterile neutrino Dark Matter. After a short introduction, we start by a general discussion of non-thermal production of Dark Matter, which applies to the three most commonly discussed mechanisms to produce sterile neutrino Dark Matter in the Universe: non-resonant, resonant, and decay production. The main goal in each case is to compute the momentum distribution function $f(p,t)$, which incorporates the full information about the Dark Matter setting under consideration, at least in what concerns its cosmological aspects. While some difficulties lie in the actual computation of this quantity, it is decisive to obtain bounds from cosmic structure formation, which turn out to be the most crucial ones to distinguish different types of production. We will introduce these bounds and we put the resulting limits into a proper context, thereby illustrating that a significant amount of relevant parameter space is available, part of which is testable in particular by Lyman-$\alpha$ data.