Dwarf spheroidal (dSph) galaxies present an evolutionary puzzle that we explore in 40 early- and late-type dwarfs in the Local Group and nearby field. Although dSphs formed stars over extended periods, today all but one are free of detectable interstellar matter (ISM), even in the Fornax dSph, where stars still formed 100 Myr ago. Combining metallicities for red giants with HI data from the literature, we show that the well-known offset in luminosity-metallicity (L-Z) relations for dSphs and dwarf irregular (dIrr) galaxies exists also when comparing only their old stellar populations: dSphs have higher mean stellar metallicities for a fixed luminosity. Evidently younger dSphs experienced more efficient enrichment than young dIrrs. Dwarf galaxies, whose locus in the L-Z diagram is consistent with that of dSphs even for baryonic luminosities, are the ``transition-type dwarfs'' Phoenix, DDO210, LGS3, Antlia, and KKR25. They have mixed dIrr/dSph morphologies, low stellar masses, low angular momentum, and HI contents of less than a few 10^6 solar masses. Unlike dIrrs, many transition-type dwarfs would closely resemble dSphs if their gas were removed; they are likely dSph progenitors. As gas removal is key, we consider the empirical evidence for various gas removal processes. We suggest that internal gas removal mechanisms are inadequate and favor ram pressure stripping to make dSphs. A combination of initial conditions and environment seems to support the formation of dSphs, which appear to form from small galaxies with active early star formation, whose evolution halts due to externally induced gas loss. Transition-type dwarfs then are dSphs that kept their ISM, and therefore should replace dSphs in isolated locations where stripping is ineffective. (Abridged)

25 pages in AASTeX two-column preprint style, 1 table, 3 figures. Accepted for publication in the Astronomical Journal (April 2003 issue)