The design of an industrial axial flow fan can take great advantage from the knowledge of performance limits and favourable design choices determined from its specific fluid-dynamic characteristics. As for other turbomachinery types, this fact is generally experienced through the entire design flow-path, from the preliminary design phase to the final optimization. Correlations, data and charts available from literature as well as proprietary database, exploited with many techniques (including machine learning) are resources in widespread use for this purpose. Despite the fluid dynamics of axial flow fans can be considered a well-known topic, nevertheless some specific points (e.g. the maximum achievable total-to-static efficiency) can be the subject of discussions, misunderstanding or bad design choices. The present work addresses this problem in two parts. In the first part a simple 1D model is built, for fans with and without stator, from classical theory of axial fans for pressure rise coefficient, head coefficient, flow angles and diffusion efficiency. The most relevant quantities (e.g. total-to-total efficiency, total-to-static efficiency), obtained with the 1D model, are plotted on hill charts as a function of the non-dimensional pressure rise and flow coefficient. This tool provides information that can be used for preliminary design evaluations, to understand and exploit the impact of the main design choices on the basic flow characteristics and the related performance. In the second part of the work a numerical investigation is presented on the main 3D flow characteristics that are observed to limit, both in CFD simulations and experimental tests, the performance of industrial axial fans at high-pressure rise and low-to-medium flow coefficients. Simulations results highlighted that local critical swirl ratios exist for the hub and the tip regions which, when exceeded, lead with different flow topology changes to a strong performance degradation.