Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute--such problems of fair division are ubiquitous. Rigorous procedures for allocating goods (or "bads" like chores), or deciding who wins on what issues in disputes, will be analyzed. Particular attention will be given to procedures that produce "envy-free' allocations, in which everybody thinks he or she received the largest portion and hence does not envy anybody else. Applications to real-life conflicts, ranging from divorce to international disputes, will be discussed.