  Dwarf galaxies play an important role in our understanding of galaxy
formation and evolution, and starbursts are believed to strongly affect their
structure and evolution. Here we present a study of 12 of the nearest dwarf
galaxies thought to be undergoing starbursts as selected primarily by
morphology. We show that these "blue amorphous galaxies" are not physically
distinguishable from dwarfs selected as starbursting by other methods, such as
blue compact dwarfs and HII galaxies. All these classes exhibit exponential
surface brightness profiles in their outer regions but often have a central
blue excess. Typically, these starbursting "cores" are young (0.01 - 0.1 Gyr)
events compared to the older (1 - 10 Gyr) enveloping galaxy. The ratio of the
core-to-envelope blue fluxes ranges from essentially zero to about two. These
starbursts are therefore modest events involving only a few percent of the
stellar mass. The envelopes have surface-brightnesses that are much higher than
typical dwarf Irregular (dI) galaxies, so it is unlikely that there is a
straightforward evolutionary relation between typical dIs and dwarf starburst
galaxies. Instead BAGs may repeatedly cycle through starburst and quiescent
phases, corresponding to the galaxies with strong and weak/absent cores
respectively. Once BAGs use up the available gas (either through star-formation
or galactic winds) so that star-formation is shut off, the faded remnants would
strongly resemble dwarf elliptical (dE) galaxies. However, in the current
cosmological epoch this is a slow process that is the aftermath of a series of
many weak, recurring bursts. Present-day dEs must have experienced more rapid
and intense evolution than this in the distant past. (Abridged)
