The review is devoted to an investigation of the behavior of vortex filaments in hard superconductors. The analysis is carried out in the region of weak magnetic fields, where linear electrodynamics is applicable. This permits a simple physical interpretation of both the properties of isolated vortices and of interactions of vortices with one another and with the surface of the superconductor. A number of examples of the influence of the superconductor outer boundary on the vortex structure are analyzed. It follows from these examples that the vortex lattice is stable relative to a transverse transport current even in an ideally homogeneous sample. Estimates are presented of the maximum transport current at which the vortex structure still remains stable. The role played by the internal surfaces in a superconductor is also illustrated with the interaction of a vortex with a cylindrical cavity or with an interface between two different superconductors as an example.