I will first start with a general introduction to theoretical ecology, stressing the reasons that make connections with statistical physics interesting and timely. I will then focus on Lotka-Volterra equations, which provide a general model to study large assemblies of strongly interacting degrees of freedom in many different fields: biology, economy, and in particular ecology. I will present our ongoing works on Lotka-Volterra equations for species-rich ecosystems. I will show that such systems display different “phases” and collective behaviors, from simple regimes with a single equilibrium to complex ones characterized by either an exponential number of multiple equilibria, all poised at the edge of stability, or chaotic dynamics. I will show how statistical physics methods allow to shed new light on open and debated questions in ecology and to provide new theoretical perspectives. Finally, I will present a study of the interplay between artificial selection at the community level and ecological dynamics.