Biomass burning is a major source of atmospheric particulate matter (PM) with impacts on health, climate, and air quality. The particles and vapors within biomass burning plumes undergo chemical and physical aging as they are transported downwind. Field measurements of the evolution of PM with plume age range from net decreases to net increases, with most showing little to no change. In contrast, laboratory studies tend to show significant mass increases on average. On the other hand, similar effects of aging on the average PM composition (e.g., oxygen-to-carbon ratio) are reported for lab and field studies. Currently, there is no consensus on the mechanisms that lead to these observed similarities and differences. This review summarizes available observations of aging-related biomass burning aerosol mass concentrations and composition markers, and discusses four broad hypotheses to explain variability within and between field and laboratory campaigns: (1) variability in emissions and chemistry, (2) differences in dilution/entrainment, (3) losses in chambers and lines, and (4) differences in the timing of the initial measurement, the baseline from which changes are estimated. We conclude with a concise set of research needs for advancing our understanding of the aging of biomass burning aerosol.