  Supersymmetric solutions, such as BPS domain walls or black holes, in four-
and five-dimensional supergravity theories with eight supercharges can be
described by effective quantum mechanics with a potential term. We show how
properties of the latter theory can help us to learn about the physics of
supersymmetric vacua and BPS solutions in these supergravity theories. The
general approach is illustrated in a number of specific examples where scalar
fields of matter multiplets take values in symmetric coset spaces.
