  In 2008, researchers at HP Labs published a paper in {\it Nature} reporting
the realisation of a new basic circuit element that completes the missing link
between charge and flux-linkage, which was postulated by Leon Chua in 1971. The
HP memristor is based on a nanometer scale TiO$_2$ thin-film, containing a
doped region and an undoped region. Further to proposed applications of
memristors in artificial biological systems and nonvolatile RAM (NVRAM), they
also enable reconfigurable nanoelectronics. Moreover, memristors provide new
paradigms in application specific integrated circuits (ASICs) and field
programmable gate arrays (FPGAs). A significant reduction in area with an
unprecedented memory capacity and device density are the potential advantages
of memristors for Integrated Circuits (ICs). This work reviews the memristor
and provides mathematical and SPICE models for memristors. Insight into the
memristor device is given via recalling the quasi-static expansion of Maxwell's
equations. We also review Chua's arguments based on electromagnetic theory.
