We are witnessing a proliferation of textured 3D models captured from the real world with automatic photo-reconstruction tools. Digital 3D models of this class come with a unique set of characteristics and defects -- especially concerning their parametrization -- setting them starkly apart from 3D models originating from other, more traditional, sources. We study this class of 3D models by collecting a significant number of representatives and quantitatively evaluating their quality according to several metrics. These include a new invariant metric we design to assess the fragmentation of the UV map, one of the main weaknesses hindering the usability of these models. Our results back the widely shared notion that such models are not fit for direct use in downstream applications (such as videogames), and require challenging processing steps. Regrettably, existing automatic geometry processing tools are not always up to the task: for example, we verify that available tools for UV optimization often fail due mesh inconsistencies, geometric and topological noise, excessive resolution, or other factors; moreover, even when an output is produced, it is rarely a significant improvement over the input (according to the aforementioned measures). Therefore, we argue that further advancements are required specifically targeted at this class of models. Towards this goal, we share the models we collected in the form of a new public repository, Real-World Textured Things (RWTT), a benchmark to systematic field-test and compare algorithms. RWTT consists of 568 carefully selected textured 3D models representative of all the main modern off-the-shelf photo-reconstruction tools. The repository is available at http://texturedmesh.isti.cnr.it/ and is browsable by metadata collected during experiments, and comes with a tool, TexMetro, providing the same set of measures for generic UV mapped datasets.