  We study the forward-backward asymmetry (AFB) and the differential branching
ratio (DBR) in B -> K* mu+ mu- in the presence of new physics (NP) with
different Lorentz structures. We consider NP contributions from vector-axial
vector (VA), scalar-pseudoscalar (SP), and tensor (T) operators, as well as
their combinations. We calculate the effects of these new Lorentz structures in
the low-q^2 and high-q^2 regions, and explain their features through analytic
approximations. We find two mechanisms that can give a significant deviation
from the standard-model predictions, in the direction indicated by the recent
measurement of AFB by the Belle experiment. They involve the addition of the
following NP operators: (i) VA, or (ii) a combination of SP and T (slightly
better than T alone). These two mechanisms can be distinguished through
measurements of DBR in B -> K* mu+ mu- and AFB in B -> K mu+ mu-.
