I review the primary methods used to determine the spin state of cometary nuclei and the pitfalls and successes experienced in their use. There are in excess of 60 reported determinations of rotational periodicities, but only a few (~4) appear to be reliable, and even these do not necessarily fully describe the true rotational state. An adequate rotational ephemeris is not, at present, available for a single cometary nucleus.
Because recent studies indicate that active cometary nuclei could be in excited spin states, I also review the theory of rigid body rotation from the point of view of remote (astronomical) observers, covering what is known of the effects of nutation on lightcurves, the influence of torques induced by jet activity, and the effects of internal energy and mass dissipation, and nuclear splitting.
The available knowledge on rotation for 8 comets, including P/Halley, is reviewed. Outstanding questions that need early resolution are: (1) Can a consensus be achieved on the rotational state of P/Halley? (2) Is it possible to accurately determine the amplitude of the transverse non-gravitational force associated with rotation? (3) Are the orientations of fan-like comas a valid indicator of the orientation of the spin vector – can definitive observational checks be made in a few cases?
Improved observational and interpretational techniques are needed to advance this field. Improved time-series and zero-date analyses are needed to connect existing and future data sets and to search for multiple periodicities in cometary lightcurves; improved sampling and extension of time-series observations with moderate- and large-aperture telescopes at good sites is needed; near-simultaneous photometric and radiometric observations made when cometary activity is low are particularly significant; well-sampled time-series imaging of near-nuclear phenomena (together with adequate software to analyze them) is essential to diagnose rotational states if nutation is present.