In this paper we review the theory of unconventional quantum critical points
that are beyond the Landau's paradigm. Three types of unconventional quantum
critical points will be discussed: (1). The transition between topological
order and semiclassical spin ordered phase; (2). The transition between
topological order and valence bond solid phase; (3). The direct second order
transition between different competing orders. We focus on the field theory and
universality class of these unconventional quantum critical points. Relation of
these quantum critical points with recent numerical simulations and experiments
on quantum frustrated magnets are also discussed.Comment: 28 pages, 6 figures. Review article for Int. J. Mod. Phys.