Grain-boundary weak links limit the critical current density of polycr
ystalline high-T-c superconductors. Themes that have evolved from rese
arch on these grain boundaries include (a) an apparent general and dra
matic distinction between the behavior of low-angle and high-angle gra
in boundaries, (b) electrical heterogeneity along as well as among bou
ndaries, (c) indications that the macroscopic current path may or may
not cross certain high-angle grain boundaries, (d) a key role for TEM-
EELS in studies of the electronic structure near grain boundaries, and
(e) evidence that current models for grain boundary structure pertain
to the high-T-c superconductors and may eventually help us to underst
and their electromagnetic character. Results regarding each of these t
opics are reviewed in this paper.