We discuss the universality classes of the local critical behavior of a bulk system near a free surface and near an internal plane of defects. A phase diagram and plausible renormalization-group flow properties for a general model which encompasses both cases are described qualitatively. Several of the crossover exponents are related to bulk critical exponents or semi-infinite surface critical exponents. The picture which is proposed accomodates systems with nonuniversal local critical exponents near a plane of defects, such as the two-dimensional Ising model near a defect line, in a natural way. Necessary conditions for nonuniversal local critical exponents and for logarithmic corrections are derived. The singularities of the energy densities near a free surface and near an internal defect plane on approaching the bulk critical temperature are analyzed.