The general phenomenology of multilayer epitaxial growth and erosion on square (001) and rectangular (110) symmetry crystal surfaces is discussed. Recently observed transitions between two kinds of ripple states on (110) surfaces are studied within a unified model. Predictions are made about several novel interface states, intervening via consecutive transitions between two rippled states on (110) surfaces. Surface morphology, coarsening dynamics, and far-from-equilibrium transitions on (001) surface are studied. Intermediary interface states with many-sided pyramids on (001) surface are predicted and characterized.