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In this paper, we demonstrate that dislocations in a macroscopic semiconductor specimen can give rise to specific mesoscopic effects. In the first place, we compare with each other two kinds of closed electron orbits that can appear in small specimens of metals and semiconductors in a magnetic field: the cyclotron orbits and the Aharonov-Bohm orbits. Next, we consider possible Aharonov-Bohm orbits encircling a dislocation in a semiconductor under a strong magnetic field whose direction is aligned with the dislocation axis. Finally, we demonstrate experiments confirming the formation of such orbits around misfit dislocations in semiconductor heterostructures with a small lattice mismatch. They manifest themselves at low temperatures as regular fluctuations of conductance through a heterostructure, appearing as a function of applied voltage and magnetic field.