We survey the problem of whether a given problem in enumerative geometry can
have all of its solutions be real. After a survey of known results, we show
how real effective rational equivalence can be used to show some enumerative
problems involving the Schubert calculus on Grassmannians may have all of
their solutions be real. This is illustrated with a new example; the
problem of 42 planes in P5 meeting 9 general planes is fully
real. We conclude with a description of the work of Ronga-Tognoli-Vust
showing that there are 5 general real conics in the plane so that all of the
3264 conics tangent to the 5 are real. A
supplement contains diagrams illustrating
some configurations of real conics. In the last section, we describe an
application of these ideas to algorithms to find exact solutions to certain
enumerative problems, and strong evidence for a conjecture of Shapiro and
Shapiro.