  Advantages of inhomogeneous cosmological models that are exact solutions of
Einstein's equations over linearised perturbations of homogeneous models are
presented. Examples of effects that can be described in the inhomogeneous ones
are given: the non-repeatable light paths, the observed anisotropies in the
cosmic microwave background, the redshift drift and the maximum diameter
distance. Criticisms of inhomogeneous models that are based on
misunderstandings or fallacious reasonings are pointed out and corrected; these
include the "weak singularity", the positivity of deceleration "theorem", the
"pathology" of redshift behaviour at the "critical point" and the alleged
necessity of the bang time to be constant.
