  This review summarizes all known results (up to this date) about methods of
integration of the classical Lotka-Volterra systems with diffusion and presents
a wide range of exact solutions, which are the most important from
applicability point of view. It is the first attempt in this direction. Because
the diffusive Lotka-Volterra systems are used for mathematical modeling
enormous variety of processes in ecology, biology, medicine, physics and
chemistry, the review should be interesting not only for specialists from
Applied Mathematics but also those from other branches of Science. The obtained
exact solutions can also be used as test problems for estimating the accuracy
of approximate analytical and numerical methods for solving relevant boundary
value problems.
