Presentation given at the "Anti-deuteron 2019" conference at UCLA (Los Angeles) on March 27, 2019. Abstract: The current generation of cosmic-ray (CR) experiments in the GeV-TeV range has reached an unprecedented level of precision, unveiling fine-details of the energy spectra. The interpretation of these measurements could require a profound revision of the widely accepted paradigm of CR acceleration at galactic sources and/or of their transport through the interstellar environments. In my talk I will discuss how AMS02 data have severely tested standard approaches to model galactic propagation in terms of scale-free diffusion and advection and I will then highlight a number of hypotheses for the origin of these new features.