  Ecosystems represent archetypal complex dynamical systems, often modelled by
coupled differential equations of the form $$ \frac{d x_i}{d t} = x_i
\varphi_i(x_1,\cdots, x_N)\ , $$ where $N$ represents the number of species and
$x_i$, the abundance of species $i$. Among these families of coupled diffential
equations, Lotka-Volterra (LV) equations $$ \frac{d x_i}{d t} = x_i ( r_i - x_i
+(\Gamma \mathbf{x})_i)\ , $$ play a privileged role, as the LV model
represents an acceptable trade-off between complexity and tractability. Here,
$r_i$ represents the intrinsic growth of species $i$ and $\Gamma$ stands for
the interaction matrix: $\Gamma_{ij}$ represents the effect of species $j$ over
species $i$. For large $N$, estimating matrix $\Gamma$ is often an overwhelming
task and an alternative is to draw $\Gamma$ at random, parametrizing its
statistical distribution by a limited number of model features. Dealing with
large random matrices, we naturally rely on Random Matrix Theory (RMT).
  The aim of this review article is to present an overview of the work at the
junction of theoretical ecology and large random matrix theory. It is intended
to an interdisciplinary audience spanning theoretical ecology, complex systems,
statistical physics and mathematical biology.
