  We present a number of conditions which are necessary for an n-dimensional
projective structure (M,[nabla]) to include the Levi-Civita connection nabla of
some metric on M. We provide an algorithm, which effectively checks if a
Levi-Civita connection is in the projective class and, in the positive, which
finds this connection and the metric. The article also provides a basic
information on invariants of projective structures, including the treatment via
Cartan's normal projective connection. In particular we show that there is a
number of Fefferman-like conformal structures, defined on a subbundle of the
Cartan bundle of the projective structure, which encode the projectively
invariant information about (M,[nabla]).
