  Enumerative Geometry is concerned with the number of solutions to a
structured system of polynomial equations, when the structure comes from
geometry. Enumerative real algebraic geometry studies real solutions to such
systems, particularly a priori information on their number. Recent results in
this area have, often as not, uncovered new and unexpected phenomena, and it is
far from clear what to expect in general. Nevertheless, some themes are
emerging.
  This comprehensive article describe the current state of knowledge,
indicating these themes, and suggests lines of future research. In particular,
it compares the state of knowledge in Enumerative Real Algebraic Geometry with
what is known about real solutions to systems of sparse polynomials.
