  We present exact spherically symmetric dyonic black hole solutions in
four-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type
potentials for the dilaton field. These solutions have unusual
asymptotics--they are neither asymptotically flat nor asymptotically (anti-) de
Sitter. The solutions have one or two horizons hiding a curvature singularity
at the origin. A class of topological dyonic black holes with topology of a
torus is also presented. Some basic properties of the black holes are
discussed.
