The general subject of this talk is the question of whether an object (such as a cake or piece of land) can be divided among N people with possibly different values so that each person receives a fair portion. Formally, there are N values (measures) on the same object - a measurable space - and a typical goal is to partition the object into N (measurable) pieces, and assign each participant a piece that he himself values at least 1/N of the total. Classical fair-division includes Steinhaus's "Ham Sandwich Problem", Dubins and Spanier’s “Sliding Knife Algorithm”, Neyman and Pearson's "Bisection Problem", and Fisher's "Problem of the Nile". Generalizations of these, in both continuous and discrete measure settings, use tools such as Lyapounov's Convexity Theorem. The talk will include several open problems, and applications to disarmament, dividing inheritances, and selection of college deans or department chairs.