The availability of increasingly large neural recordings in vivo, as well as fully controllable in-silico models, may allow addressing a key question in theoretical neuroscience and artificial intelligence: how neuronal units collectively represent relevant information. However, data alone are not sufficient for this purpose: one needs reliable tools to explore the latent geometry of high-dimensional neural data. A starting point of such exploration is characterizing the intrinsic dimension (ID) of neural manifolds. This indicator could provide immediate information about the minimum number of encoded variables, the relation between collective and individual neural patterns, and the balance between efficiency and robustness in the neural code. However, three main obstacles stand in the way of a correct estimation of the ID: nonlinearity (or curvature), density variations, and undersampling. In this seminar, I will discuss how current estimators may circumvent each of this obstacles separately, under specific assumptions, while no existing method can jointly overcome all the obstacles. This challenge will be illustrated through examples taken from my latest work on the ID of artificial recurrent neural networks performing simple tasks and large-scale neuronal recordings in vivo.