  We present a semiclassical study of a transport process, the tunneling, in
the presence of a magnetic field and a dissipative environment. We have found
that the problem can be mapped onto an effective one-dimensional one, and the
tunneling rate is strongly affected by the magnetic field, such as a complete
suppression by a large parallel magnetic field, an example of the dynamical
localization. In such case a small perpendicular component of the field, or the
dissipation, can enhance the tunneling rate. In the small parallel field and
finite temperatures the tunneling rate is finite. Explicit expressions will be
presented in those cases. If viewing the tunneling in the presence of a
magnetic field as a dissipative tunneling process, by varying the magnetic
field and the potential one can obtain the dissipative spectral function
between the subohmic $s =0$ and the superohmic $s = \infty$. In combination
with a real dissipative spectral function, the effect of the magnetic field can
map the spectral function from $s $ to $2-s$, with $s>2$ mapping to $ s = 0$,
revealing a dual symmetry between the friction and the Lorentz force. Two cases
relevant to experiments, the edge state tunneling in a Hall bar and the
tunneling near the dynamical localization will be discussed in detail.
