  Anomalous Microwave Emission (AME) is a component of diffuse Galactic
radiation observed at frequencies in the range $\approx 10$-60 GHz. AME was
first detected in 1996 and recognised as an additional component of emission in
1997. Since then, AME has been observed by a range of experiments and in a
variety of environments. AME is spatially correlated with far-IR thermal dust
emission but cannot be explained by synchrotron or free-free emission
mechanisms, and is far in excess of the emission contributed by thermal dust
emission with the power-law opacity consistent with the observed emission at
sub-mm wavelengths. Polarization observations have shown that AME is very
weakly polarized ($\lesssim 1$%). The most natural explanation for AME is
rotational emission from ultra-small dust grains ("spinning dust"), first
postulated in 1957. Magnetic dipole radiation from thermal fluctuations in the
magnetization of magnetic grain materials may also be contributing to the AME,
particularly at higher frequencies ($\gtrsim 50$ GHz). AME is also an important
foreground for Cosmic Microwave Background analyses. This paper presents a
review and the current state-of-play in AME research, which was discussed in an
AME workshop held at ESTEC, The Netherlands, June 2016.
