  Modern observations based on general relativity indicate that the spatial
geometry of the expanding, large-scale Universe is very nearly Euclidean. This
basic empirical fact is at the core of the so-called "flatness problem", which
is widely perceived to be a major outstanding problem of modern cosmology and
as such forms one of the prime motivations behind inflationary models. An
inspection of the literature and some further critical reflection however
quickly reveals that the typical formulation of this putative problem is
fraught with questionable arguments and misconceptions and that it is moreover
imperative to distinguish between different varieties of problem. It is shown
that the observational fact that the large-scale Universe is so nearly flat is
ultimately no more puzzling than similar "anthropic coincidences", such as the
specific (orders of magnitude of the) values of the gravitational and
electromagnetic coupling constants. In particular, there is no fine-tuning
problem in connection to flatness of the kind usually argued for. The arguments
regarding flatness and particle horizons typically found in cosmological
discourses in fact address a mere $single$ issue underlying the standard FLRW
cosmologies, namely the $extreme$ improbability of these models with respect to
any "reasonable measure" on the "space of all spacetimes". This issue may be
expressed in different ways and a phase space formulation, due to Penrose, is
presented here. A horizon problem only arises when additional assumptions -
which are usually kept implicit and at any rate seem rather speculative - are
made.
