Classical continuum theory is generalized to provide a systematic procedure for treating in successively greater detail the macroscopic manifestations of subcontinuum events without sacrificing the convenience of the field approach. The point of departure from traditional theory is the general angular momentum principle for continua. Internal angular momentum is associated with configurational and kinematic structure of the continuum `particle' and that structure is represented by moment expansions in polyadic polarization densities. Each step in the theoretical development is analyzed both in terms of the statistical mechanics of polyatomic media and from the standpoint of continuum physics. Accurate accounting of content and flux is found to require introducing the concepts of proper densities and currents. Among topics examined in detail are asymmetric states of stress, equations of change for dynamical variables, and equilibrium conditions in structured continua, including alinement of internal angular momentum with the principle axes of local mass distributions.