We propose a quantum theory of rotating light beams and study some of its properties. Such beams are
polychromatic and have either a slowly rotating polarization or a slowly rotating transverse mode pattern. We
show there are, for both cases, three different natural types of modes that qualify as rotating, one of which is a
new type not previously considered. We discuss differences between these three types of rotating modes on the
one hand and non-rotating modes as viewed from a rotating frame of reference on the other, thus resolving some
paradoxes mentioned recently.