The classical problem of enumerating rational curves in projective spaces is solved using a recursion formula for Gromov-Witten invariants. In this talk, I will describe a similar relation for real Gromov-Witten invariants with conjugate pairs of constraints. An application of this relation provides a complete recursion for counts of real rational curves with such constraints in odd-dimensional projective spaces. I will outline the proof and discuss some vanishing and non-vanishing results. This is joint work with A. Zinger.