  The star formation histories of Local Group (LG) dwarf galaxies and more
distant potential LG members are reviewed. Problems in defining the spatial
extent of the LG and membership are briefly discussed. The morphological types
found in the LG are presented, and it is suggested that we see continuous
evolution from low-mass dwarf irregulars (dIrrs) to dwarf spheroidal galaxies
(dSph) in the LG.
  Star formation histories for LG dwarfs and nearby LG candidates are compiled
using population boxes. No two dwarfs, irrespective of morphological type, show
the same evolutionary history, and all vary widely in ages of their
subpopulations and in their enrichment history. The lack of gas in dSphs and
dEs may be explained by a new photoionization scenario. Old populations, often
spatially very extended, may be a common property of dwarf galaxies, though
their fractions can be very small. Almost all types of dwarf galaxies studied
in detail so far show spatial variations in ages and abundances such as radial
age/metallicity gradients. The observed star formation histories impose
constraints on merger and accretion scenarios.
  Properties of the Milky Way dSphs are compared to the M31 dSphs and discussed
in the framework of the ram pressure/tidal stripping scenario. It is
demonstrated that the newly discovered LG dwarfs follow the same relationship
for central surface brightness, mean metallicity, and absolute magnitude as the
other LG dwarfs. (Shortened)
