We are witnessing a proliferation of textured 3D models captured from the real world with automatic photo-reconstruction tools by people and professionals without a proper technical background in computer graphics. 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 carefully design to assess the amount of fragmentation of the UV map, which is one of the main weaknesses potentially hindering the usability of these models. Our results back the widely shared notion that models of this new class are still 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 the available tools for UV optimization often fail due to mesh inconsistencies, geometric and topological noise, excessive resolution, or other factors; moreover, even when an output is produced, it rarely represents a significant improvement over the input (according to the aforementioned measures). Therefore, we argue that further advancements are required by the computer graphics and geometry processing communities specifically targeted at this class of models. Towards this goal, we share the models we collected in this study as a new public repository, Real-World Textured Things (RWTT), intended as a benchmark to systematic field-test and compare future algorithms. RWTT consists of 568 carefully selected textured 3D models representative of the most popular photo-reconstruction tools currently available. We also provide a web interface to browse the dataset by the metadata we collected during our experiments and a tool, TexMetro, to compute the same set of measures on generic UV mapped datasets. The Real-World Textured Things (RWTT) Dataset is available at https://texturedmesh.isti.cnr.it/ https://doi.org/10.1016/j.cagd.2020.101943/