Abstract: Front propagation into unstable states often mediates state transitions in spatially extended systems, in biological models and across the sciences. Classical examples include the Fisher-KPP equation for population genetics, Lotka-Volterra models for competing species, and Keller-Segel models for bacterial motion in the presence of chemotaxis. A fundamental question is to predict the speed of the propagating front as well as which new state is selected in its wake. The marginal stability conjecture asserts that front invasion speeds are determined by the spectrum of the linearization about traveling wave solutions of the PDE model. We present a formulation and proof of the marginal stability conjecture in general reaction-diffusion systems, and give an outlook towards establishing invasion properties in complex pattern-forming systems.