Chemical erosion of a porous medium is a complex process, involving
the interplay between flow, transport, reaction and geometry
evolution. The nonlinear couplings between these processes may lead to
the formation of intricate dissolution patterns, the characteristics
of which depend strongly on the fluid flow and mineral dissolution
rates. In particular, in a broad range of physical conditions, long,
finger-like channels or ``wormholes'' are spontaneously formed, where
the majority of the flow is focused. It is hypothesized that the
appearance of this structures stands behind the formation of conduits
in limestone caves. Formation of wormholes is also important for the
petrolum industry, where they are used to increase the effectiveness
of oil extraction from reservoirs. We analyze the process of wormhole
formation by a combination of numerical modeling, experiments and
theoretical work.