  Two anomalies at nuclear reactors, one related to the absolute antineutrino
flux, one related to the antineutrino spectral shape, have drawn special
attention to the field of reactor neutrino physics during the past decade.
Numerous experimental efforts have been launched to investigate the reliability
of flux models and to explore whether sterile neutrino oscillations are at the
base of the experimental findings. This review aims to provide an overview on
the status of experimental searches at reactors for sterile neutrino
oscillations and measurements of the antineutrino spectral shape in mid-2021.
The individual experimental approaches and results are reviewed. Moreover,
global and joint oscillation and spectral shape analyses are discussed. Many
experiments allow setting constraints on sterile oscillation parameters, but
cannot yet cover the entire relevant parameter space. Others find evidence in
favour of certain parameter space regions. In contrast, findings on the
spectral shape appear to give an overall consistent picture across experiments
and allow narrowing down contributions of certain isotopes.
