  Neutrinos, being the only fermions in the Standard Model of Particle Physics
that do not possess electromagnetic or color charges, have the unique
opportunity to communicate with fermions outside the Standard Model through
mass mixing. Such Standard Model-singlet fermions are generally referred to as
"sterile neutrinos''. In this review article, we discuss the theoretical and
experimental motivation for sterile neutrinos, as well as their
phenomenological consequences. With the benefit of hindsight in 2020, we point
out potentially viable and interesting ideas. We focus in particular on sterile
neutrinos that are light enough to participate in neutrino oscillations, but we
also comment on the benefits of introducing heavier sterile states. We discuss
the phenomenology of eV-scale sterile neutrinos in terrestrial experiments and
in cosmology, we survey the global data, and we highlight various intriguing
anomalies. We also expose the severe tension that exists between different data
sets and prevents a consistent interpretation of the global data in at least
the simplest sterile neutrino models. We discuss non-minimal scenarios that may
alleviate some of this tension. We briefly review the status of keV-scale
sterile neutrinos as dark matter and the possibility of explaining the
matter-antimatter asymmetry of the Universe through leptogenesis driven by yet
heavier sterile neutrinos.
