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Modern observations based on general relativity indicate that the spatialgeometry of the expanding, large-scale Universe is very nearly Euclidean. Thisbasic empirical fact is at the core of the so-called "flatness problem", whichis widely perceived to be a major outstanding problem of modern cosmology andas such forms one of the prime motivations behind inflationary models. Aninspection of the literature and some further critical reflection howeverquickly reveals that the typical formulation of this putative problem isfraught with questionable arguments and misconceptions and that it is moreoverimperative to distinguish between different varieties of problem. It is shownthat the observational fact that the large-scale Universe is so nearly flat isultimately no more puzzling than similar "anthropic coincidences", such as thespecific (orders of magnitude of the) values of the gravitational andelectromagnetic coupling constants. In particular, there is no fine-tuningproblem in connection to flatness of the kind usually argued for. The argumentsregarding flatness and particle horizons typically found in cosmologicaldiscourses in fact address a mere $single$ issue underlying the standard FLRWcosmologies, namely the $extreme$ improbability of these models with respect toany "reasonable measure" on the "space of all spacetimes". This issue may beexpressed in different ways and a phase space formulation, due to Penrose, ispresented here. A horizon problem only arises when additional assumptions -which are usually kept implicit and at any rate seem rather speculative - aremade.

How Problematic is the Near-Euclidean Spatial Geometry of the Large-Scale Universe?