Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and crossdisciplinary applications, including reduced-variable models of combustion flames, Reid’s paradox of rapid forest range expansions, the European colonization of North America during the XIX century, the Neolithic transition in Europe from 13,000 to 5,000 years before present, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure, systems with several interacting species, etc. Directions for future progress are outlined.