  A series of experiments studying neutrinos from intense radioactive sources
have reported a deficit in the measured event rate which, in combination, has
reached a statistical significance of $\sim 5\sigma$. In this paper, we explore
avenues for explaining this anomaly, both within the Standard Model and beyond.
First, we discuss possible biases in the predicted cross section for the
detection reaction $\nu_e + ^{71}\text{Ga} \to e^- + ^{71}\text{Ge}$, which
could arise from mismeasurement of the inverse process, $^{71}\text{Ge}$ decay,
or from the presence of as yet unknown low-lying excited states of
$^{71}\text{Ga}$. The latter would imply that not all $^{71}\text{Ge}$ decays
go to the ground state of $^{71}\text{Ga}$, so the extraction of the ground
state-to-ground state matrix element relevant for neutrino capture on gallium
would be incorrect. Second, we scrutinize the measurement of the source
intensity in gallium experiments, and we point out that a $\sim 2\%$ error in
the branching ratios for $^{51}\text{Cr}$ decay would be enough to explain the
anomaly. Third, we investigate the calibration of the radiochemical germanium
extraction efficiency as a possible origin of anomaly. Finally, we outline
several new explanations beyond the Standard Model, including scenarios with
sterile neutrinos coupled to fuzzy dark matter or to dark energy, as well as a
model with decaying sterile neutrinos. We critically assess the viability of
these scenarios, and others that have been proposed, in a summary table.
