  A circularly polarized electromagnetic plane wave carries an electric field
that rotates clockwise or counterclockwise around the propagation direction of
the wave. According to the handedness of this rotation, its \emph{longitudinal}
spin angular momentum density is either parallel or antiparallel to the
propagation of light. However, there are also light waves that are not simply
plane and carry an electric field that rotates around an axis perpendicular to
the propagation direction, thus yielding \emph{transverse} spin angular
momentum density. Electric field configurations of this kind have been
suggestively dubbed "photonic wheels". It has been recently shown that photonic
wheels are commonplace in optics as they occur in electromagnetic fields
confined by waveguides, in strongly focused beams, in plasmonic and evanescent
waves. In this work we establish a general theory of electromagnetic waves
{propagating along a well defined direction, which carry} transverse spin
angular momentum density. We show that depending on the shape of {these waves,
the} spin density may be either perpendicular to the \emph{mean} linear
momentum (globally transverse spin) or to the linear momentum \emph{density}
(locally transverse spin). We find that the latter case generically occurs only
for non-diffracting beams, such as the Bessel beams. Moreover, we introduce the
concept of \emph{meridional} Stokes parameters to operationally quantify the
transverse spin density. To illustrate our theory, we apply it to the exemplary
cases of Bessel beams and evanescent waves. These results open a new and
accessible route to the understanding, generation and manipulation of optical
beams with transverse spin angular momentum density.
