This chapter explains why atom jumps with a vacancy mechanism are not random, even if the vacancy itself moves by random walk. In an alloy with chemical interactions strong enough to cause a phase transformation, the vacancy frequently resides at energetically favorable locations, so any assumption of random walk can be seriously in error. When materials with different diffusivities are brought into contact, their interface is displaced with time because the fluxes of atoms across the interface are not equal in both directions. Even the meaning of the interface, or at least its position, requires new concepts. An applied field can bias the diffusion process towards a particular direction, and such a bias can also be created by chemical interactions between atoms. When thermal atom diffusion occurs in parallel with atom jumps forced without thermal activation, a steady state can be calculated, but it is not a state of thermodynamic equilibrium. Finally, the venerable statistical mechanics model of diffusion by Vineyard is described.