  Bosonization of degenerate fermions yields insight both into Landau Fermi
liquids, and into non-Fermi liquids. We begin our review with a pedagogical
introduction to bosonization, emphasizing its applicability in spatial
dimensions greater than one. After a brief historical overview, we present the
essentials of the method. Well known results of Landau theory are recovered,
demonstrating that this new tool of many-body theory is robust. Limits of
multidimensional bosonization are tested by considering several examples of
non-Fermi liquids, in particular the composite fermion theory of the
half-filled Landau level. Nested Fermi surfaces present a different challenge,
and these may be relevant in the cuprate superconductors. We conclude by
discussing the future of multidimensional bosonization.
