  Analytical models describing the dynamics of lobed radio sources are
essential for interpretation of the tens of millions of radio sources that will
be observed by the Square Kilometre Array and pathfinder instruments. We
propose that historical models can be grouped into two classes in which the
forward expansion of the radio source is driven by either the jet momentum flux
or lobe internal pressure. The most recent generation of analytical models
combines these limiting cases for a more comprehensive description. We extend
the mathematical formalism of historical models to describe source expansion in
non-uniform environments, and directly compare different model classes with
each other, and with hydrodynamic numerical simulations. We quantify
differences in predicted observable characteristics for lobed radio sources due
to the different model assumptions for their dynamics. We make our code for the
historical models analysed in this review openly available to the community.
