Knowledge of the zeros of a statistical mechanics partition function is mainly useful for telling us what singularities {\it  do not} occur as some parameter (such as magnetic field) is varied.  Reflection positivity, on the other hand, can sometimes tell us what singularities do occur, especially as concerns phase transitions and long-range-order. (Exceptionally, both are valid for the Ising model.) I will not say anything about zeros, but I will try to explain RP and give one example in which it works: how RP proves alignment of interacting dimers (with O. Heilmann).