  This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body
dynamics and presents some new results. As is well known, the problem of
unsupported and unperturbed rigid rotator can be reduced. The availability of
this reduction is offered by the underlying symmetry, which stems from
conservation of the angular momentum and rotational kinetic energy. When a
perturbation is turned on, these quantities are no longer preserved.
Nonetheless, the language of reduced description remains extremely instrumental
even in the perturbed case. We describe the canonical reduction performed by
the Serret-Andoyer (SA) method, and discuss its applications to attitude
dynamics and to the theory of planetary rotation. Specifically, we consider the
case of angular-velocity-dependent torques, and discuss the
variation-of-parameters-inherent antinomy between canonicity and osculation.
Finally, we address the transformation of the Andoyer variables into the
action-angle ones, using the method of Sadov.
