  The Universe is not completely homogeneous. Even if it is sufficiently so on
large scales, it is very inhomogeneous at small scales, and this has an effect
on light propagation, so that the distance as a function of redshift, which in
many cases is defined via light propagation, can differ from the homogeneous
case. Simple models can take this into account. I review the history of this
idea, its generalization to a wide variety of cosmological models, analytic
solutions of simple models, comparison of such solutions with exact solutions
and numerical simulations, applications, simpler analytic approximations to the
distance equations, and (for all of these aspects) the related concept of a
"Swiss-cheese" universe.
