  In this paper we revisit the memristor concept within circuit theory. We
start from the definition of the basic circuit elements, then we introduce the
original formulation of the memristor concept and summarize some of the
controversies on its nature. We also point out the ambiguities resulting from a
non rigorous usage of the flux linkage concept. After concluding that the
memristor is not a fourth basic circuit element, prompted by recent claims in
the memristor literature, we look into the application of the memristor concept
to electrophysiology, realizing that an approach suitable to explain the
observed inductive behavior of the giant squid axon had already been developed
in the 1960s, with the introduction of "time-variant resistors." We also
discuss a recent memristor implementation in which the magnetic flux plays a
direct role, concluding that it cannot strictly qualify as a memristor, because
its $v-i$ curve cannot exactly pinch at the origin. Finally, we present
numerical simulations of a few memristors and memristive systems, focusing on
the behavior in the $\varphi-q$ plane. We show that, contrary to what happens
for the most basic memristor concept, for general memristive systems the
$\varphi-q$ curve is not single-valued or not even closed.
