Branching random walks are systems of particles which branch and diffuse randomly. They arise in many different contexts such as population models, disordered systems in statistical physics or reaction-diffusion equations. We speak of a heterogeneous environment if the reproduction or the motion of the particles depends on space and/or time on a macroscopic scale. This extra freedom is useful from a modelling perspective, moreover, these models exhibit a much wider range of behaviour than the classical branching random walk. In this talk, I will review their basic properties and present two recent results. The first concerns the efficiency of algorithms for finding low-energy states in Derrida?s continuous random energy model, a Gaussian branching random walk with time-dependent variance. The second concerns the speed of propagation of branching random walks with local selection in heterogenous environment. Based on joint work with (first) Louigi Addario-Berry and (second) Gaël Raoul and Julie Tourniaire.