The origin and evolution of dwarf galaxies is one of the key issues in galaxy evolution today. In standard hierarchical galaxy formation models, low mass galaxies play a crucial role in the formation and evolution of all types of galaxies. Thus, it is necessary to understand the onset and propagation of star formation in low mass galaxies to model correctly galaxy evolution on all size scales. I will present the results of several recent studies of the star formation process in nearby dwarf galaxies which indicate that the gas surface density is too low to support efficient percolation of star formation activity across the disk, suggesting that star formation is a local, not global, process. Further, I will discuss the apparent structural differences between typical dwarf irregular galaxies and the class of starbursting dwarf galaxies which suggest that most dwarf galaxies do not go through a starburst phase. Finally, I will discuss the results of recent kinematic observations of dwarf elliptical galaxies in the Virgo cluster to examine dynamical constraints on dwarf galaxy evolution and to explore possible evolutionary connections between gas-rich and gas-poor dwarf galaxies in the local universe.