What is the maximal number of real solutions to a sparse polynomial system (2.1) with common Newton polytope P? The situation here is far from settled. There are constructive lower bounds, which are not optimal, which we discuss in Section 2.iii.a. There is a non-trivial upper bound from the theory of fewnomials, which is almost surely not sharp, and finally there is an intriguing conjecture of Kushnirenko, proposing better upper bounds, but that conjecture is false.