  In this Chapter, we present our latest experimental results (along with their
theoretical interpretation) related to some unusual magnetic properties of
artificially prepared ordered two-dimensional Josephson junction arrays (of
both shunted and unshunted Nb-AlO_x-Nb tunnel junctions). Namely, we address
the following topics: (i) influence of non-uniform critical current density
profile on magnetic field behavior of AC susceptibility, (ii) origin of the
so-called dynamic reentrance phenomenon, and (iii) manifestation of novel
geometric quantization effects in temperature behavior of AC magnetic response.
