  Local propagation and energy flux in structured optical fields is often
associated with the Poynting vector. However, the local phase gradient (i.e.,
local wavevector) in monochromatic fields in free space is described by another
fundamental quantity: the canonical momentum density. The distributions of the
Poynting and canonical momentum densities can differ significantly from each
other in structured fields. We examine the role of these quantities in the
propagation and diffraction of structured optical fields, exemplified by
various circularly-polarized vortex beams carrying orbital angular momentum. We
describe the canonical and Poynting momentum distributions in such beams,
experimentally measure the local transverse momentum density by Shack-Hartmann
wavefront sensor, and investigate fine features of the diffraction of various
vortex beams on a knife-edge aperture. In all cases, the measured local
momentum density and local beam evolution are consistent with the canonical
momentum distribution rather than the Poynting vector. Furthermore, we
introduce the local angular velocity in vortex beams and determine the
universal integral $\pi$ angle of azimuthal rotation in an arbitrary (yet
circularly-symmetric) propagating and diffracting vortex beam. Finally, we
discuss the "supermomentum" and "backflow" effects; both of these phenomena are
examples of superoscillations and are related to the properties of the
canonical momentum. Our results reveal the profound role of the canonical
momentum in the evolution of light and demonstrate the importance of
distinguishing between it and the Poynting vector in structured light.
