In this review I summarise recent advances in our understanding of the importance of starburst events to the evolutionary histories of nearby galaxies. Ongoing bursts are easily diagnosed in emission-line surveys, but assessing the timing and intensity of fossil bursts requires more effort, usually demanding color-magnitude diagrams or spectroscopy of individual stars. For ages older than ~1 Gyr, this type of observation is currently limited to the Local Group and its immediate surroundings. However, if the Local Volume is representative of the Universe as a whole, then studies of the age and metallicity distributions of star clusters and resolved stellar populations should give statistical clues as to the frequency and importance of bursts to the histories of galaxies in general. Based on starburst statistics in the literature and synthetic colour-magnitude diagram studies of Local Group galaxies, I attempt to distinguish between systemic starbursts that strongly impact galaxy evolution and stochastic bursts that can appear impressive but are ultimately of little significance on gigayear timescales. As a specific case, it appears as though IC 10, the only starburst galaxy in the Local Group, falls into the latter category and is not fundamentally different from other nearby dwarf irregular galaxies. ; Comment: Accepted by the Publications of the Astronomical Society of Australia (PASA). Summary of a review talk given at the Southern Cross Astrophysics Conference on "Galaxy Metabolism" held in Sydney, 22-26 June 2009. 9 pages, 2 figures