We report recent advances concerning the package allocation problem, in which traders seek to buy or sell combinations of goods. The problems are most difficult when some goods are not substitutes. In that case, competitive equilibrium typically fail to exist but the core is non-empty and comprises the competitive solutions. Also in that case, the Vickrey auction fails to select core allocations and yield revenues that are less than competitive. The Ausubel-Milgrom auction generally selects core allocations and, when goods are substitutes, prescribes the Vickrey allocation. We also evaluate the problems and promise of mechanisms for the package exchange problem.