We briefly review aspects of superconductive persistent currents in Josephson junctions of the S/I/S, S/O/S and S/N/S types, focusing on the origin of jumps in the current versus phase dependences, and discuss in more detail the persistent as well as «spontaneous» currents in the Aharonov-Bohm mesoscopic and nanoscopic (macromolecular) structures. A fixed-number-of- electrons mesoscopic or macromolecular conducting ring is shown to be unstable against structural transformation removing spatial symmetry (in particular, azimuthal periodicity) of its electron-lattice Hamiltonian. In case when the transformation is blocked by strong coupling to an external azimuthally symmetric environment, the system becomes bistable in its electronic configuration at certain number of electrons. At such a condition, the persistent current has a nonzero value even at the (almost) zero applied Aharonov-Bohm flux, and results in very high magnetic susceptibility dM/dH at small nonzero fields, followed by an oscillatory dependence at larger fields. We tentatively assume that previously observed oscillatory magnetization in cyclic metallo-organic molecules by Gatteschi et al. can be attributed to persistent currents. If this proves correct, it may open an opportunity (and, more generally, macromolecular cyclic structures may suggest the possibility) of engineering quantum computational tools based on the Aharonov-Bohm effect in ballistic nanostructures and macromolecular cyclic aggregates.