  MOND is a phenomenological modification of Newton's law of gravitation which
reproduces the dynamics of galaxies, without the need for additional dark
matter. This paper reviews the basics of MOND and its application to dwarf
galaxies. MOND is generally successful at reproducing stellar velocity
dispersions in the Milky Way's classical dwarf ellipticals, for reasonable
values of the stellar mass-to-light ratio of the galaxies; two discrepantly
high mass-to-light ratios may be explained by tidal effects. Recent
observations also show MOND describes tidal dwarf galaxies, which form in
complex dynamical environments. The application of MOND to galaxy clusters,
where it fails to reproduce observed gas temperatures, is also reviewed.
Relativistic theories containing MOND in the non-relativistic limit have now
been formulated; they all contain new dynamical fields, which may serve as
additional sources of gravitation that could reconcile cluster observations
with MOND. Certain limits of these theories can also give the accelerating
expansion of the Universe. The standard dark matter cosmology boasts numerous
manifest triumphs; however, alternatives should also be pursued as long as
outstanding observational issues remain unresolved, including the empirical
successes of MOND on galaxy scales and the phenomenology of dark energy.
