The topic of this survey article has seen a renaissance during the past couple of years. Here we present and extend the results for various phenomena which we have published from 2012-2014, with gratitude to our coauthors. The new phenomena include (a) the first reduced nuclear flux densities in vibrating diatomic molecules or ions which have been deduced from experimental pump–probe spectra; these "experimental" nuclear flux densities reveal several quantum effects including (b) the "quantum accordion", i.e., during the turn from bond stretch to bond compression, the diatomic system never stands still - instead, various parts of it with different bond lengths slow into opposite directions. (c) Wavepacket interferometry has been extended from nuclear densities to flux densities, again revealing new phenomena: For example, (d) a vibrating nuclear wave function with compact initial shape may split into two partial waves which run into opposite directions, thus causing interfering flux densities. (e) Tunneling in symmetric 1-dimensional double-well systems yields maximum values of the associated nuclear flux density just below the potential barrier; this is in marked contrast with negligible values of the nuclear density just below the barrier. (f) Nuclear flux densities of pseudorotating nuclei may induce huge magnetic fields. A common methodologic theme of all topics is the continuity equation which connects the time derivative of the nuclear density to the divergence of the flux density, subject to the proper boundary conditions. (g) Nearly identical nuclear densities with different boundary conditions may be related to entirely different flux densities, e.g., during tunneling in cyclic versus non-cyclic systems. The original continuity equation, density and flux density of all nuclei, or of all nuclear degrees of freedom, may be reduced to the corresponding quantities for just a single nucleus, or just a single degree of freedom.