  This paper is concerned with the dynamics and interactions of Q-balls in
(1+1)-dimensions. The asymptotic force between well-separated Q-balls is
calculated to show that Q-balls can be attractive or repulsive depending upon
their relative internal phase. An integrable model with exact multi-Q-ball
solutions is investigated and found to be of use in explaining the dynamics in
non-integrable theories. In particular, it is demonstrated that the dynamics of
small Q-balls in a generic class of non-integrable models tends towards
integrable dynamics as the charge decreases. Long-lived oscillations of a
single Q-ball can also be understood in terms of a deformation of an exact
breather solution in the integrable model. Finally, we show that any theory
with Q-ball solutions has a dual description in which a stationary Q-ball is
dual to a static kink, with an interchange of Noether and topological charges.
