  The jet shape is a simple measure of how widely a jet's energy is spread. At
present jet shape distributions have only been calculated to leading order in
perturbative QCD. In this paper we consider how much these predictions should
be affected by higher order perturbative corrections, by resummation of
enhanced corrections to all orders, and by (power-suppressed) non-perturbative
corrections. We also show that current cone-type jet definitions are not
infrared safe for final states with more than three partons. Unless this
situation is rectified by using improved definitions, hadron collider
experiments will never be able to study the internal properties of jets with
the quantitative accuracy already achieved in $e^+e^-$ annihilation.
