The dynamical evolution of short-period comets, and in particular of those belonging to the so-called Jupiter family, is reviewed. Encounters with Jupiter play a dominant role in determining the
dynamical fate of these objects, although, in some peculiar cases, also interactions with other planets may be important. Frequent although temporary librations around resonances with Jupiter are displayed by more than one third of short-period comets. Integrations of motion of observed comets, over a time span comparable with their lifetime as active objects, are compared with previous numerical investigations, to get insight into the non observed phases of the dynamical evolution of these objects.
Theories of the origin of the Oort ctoud are examined in the light of recent observations of comets and of star-forming environments, and some popular hypotheses are found to meet with difficulties. In particular chemical and experimental evidence that comets grow in an extremely cold, quiescent environment is proving difficult to reconcile with recent CO and IR observations showing that the environment of a star-forming region is characterised by turbulent,
high-velocity flows and that young stars are prone to recurrent, violent outbursts. The aggregation around young stars of
planetesimals pre-existing in molecular ciouds avoids these problems. However formed, the Oort cloud is disturbed through
interactions with its galactic environment. A record of these past disturbances, episodic or regular, is in principle recoverable through impact cratering and other geological signatures, and these terrestrial records therefore provide a further new constraint on the structure and evolution of the Oort cloud. The concepts of
r 'dense inner cloud' or a 'solar companion star' are difficult to reconcile with the impact cratering history. The debris from the very largest comets are expected to play a dominant role in producing galactic modulations of such fundamental phenomena as the rise and fali of oceans, ice ages, geomagnetic reversals and the origin of life. A ~15 Myr galactic cycle in particular is predicted. Power spectrum analyses applied to cratering, vulcanism and geomagnetic reversal records for the last -200 Myr reveal the presence of a 16 ± 2 Myr cycle.