The effect of dielectric boundaries on the Cherenkov radiation (CR) produced when a fast point charge moves inside or near a material is analyzed for different shapes of the sample. Calculations are offered for a charge moving near both planar and nonplanar surfaces. CR is found to be produced even when the external charge moves outside a semi-infinite medium. For charges moving near planar boundaries, the reflected radiation interferes with the direct CR, leading to oscillations in the emission probability as a function of the impact parameter relative to the interfaces. Thin-film guided modes are excited by penetrating electrons and our calculations agree reasonably well with available experiments. The bulk limit in the emission probability is recovered for charges passing by the center of cylinders or spheres of increasingly large radius. Recent experiments of energy loss of electrons passing near dielectric spheres are explained thanks to the inclusion of retardation effects in the sphere response. These effects lead to an efficient channel of radiative energy losses. Finally, the diffraction of CR in void inclusions is proposed as a tool for providing information on otherwise inaccessible buried structures. Help and support from the Basque Departamento de Educacion, Universidades e Investigacion, the University of the Basque Country UPV/EHU Contract No. 00206.215-13639/2001, and the Spanish Ministerio de Ciencia y Tecnologia Contract No. MAT2001-0946 is gratefully acknowledged. Peer reviewed