It is widely appreciated that population waves have played a crucial role in the evolutionary history of many species. Genetic footprints of many pioneer species are still recognizable today, and neutral genetic markers can be used to infer information about growth, ancestral population size, colonization pathways, etc. Bacterial growth on a Petri dish can be used to model this phenomenon, using the change of a single amino acid residue in a fluorescent protein encoded on a plasmid as a marker. The frontier of acts as a moving genetic bottleneck, and neutral mutations optimally positioned on the edge of a growing population wave can increase their abundance via a ``surfing'' phenomenon. Striking patterns of gene segregation and lineage histories are observed for both radial and linear inoculations of populations of bacteria and yeast. Recent experimental and theoretical studies of this effect will be presented, using bacteria and yeast as model systems, including results for surfing of deleterious and favorable mutations during range expansion.