  Over the past decade, materials that combine broken inversion symmetry with
metallic conductivity have gone from a thought experiment to one of the fastest
growing research topics. In 2013, the observation of the first uncontested
polar transition in a metal, LiOsO$_3$, inspired a surge of theoretical and
experimental work on the subject, uncovering a host of materials which combine
properties previously thought to be contraindicated [Nat. Mater. \textbf{12},
1024 (2013)]. As is often the case in a nascent field, the sudden rise in
interest has been accompanied by diverse (and sometimes conflicting)
terminology. Although ``ferroelectric-like" metals are well-defined in theory,
i.e., materials that undergo a symmetry-lowering transition to a polar phase
while exhibiting metallic electron transport, real materials find a myriad of
ways to push the boundaries of this definition. Here, we review and explore the
burgeoning polar metal frontier from the perspectives of theory, simulation,
and experiment while introducing a unified taxonomy. The framework allows one
to describe, identify, and classify polar metals; we also use it to discuss
some of the fundamental tensions between theory and models of reality inherent
in the terms ``ferroelectric" and ``metals.'' In addition, we highlight
shortcomings of electrostatic doping simulations in modeling different
subclasses of polar metals, noting how the assumptions of this approach depart
from experiment. We include a survey of known materials that combine polar
symmetry with metallic conductivity, classified according to the mechanisms
used to harmonize those two orders and their resulting properties. We conclude
by describing opportunities for the discovery of novel polar metals by
utilizing our taxonomy.
