Very-high-energy gamma rays and neutrinos are crucial messengers for assessing the PeVatron nature of cosmic sources. In particular, supernova remnants (SNRs) are since long time believed to be the major contributors to the Galactic cosmic-ray flux observed at Earth. Despite experimental efforts devoted to the identification of PeV activity in SNRs, such a picture remains yet to be confirmed. Additionally, the poor knowledge of the magnetic turbulence development and evolution in these sources still prevent us from a full understanding of the process of particle acceleration and propagation at SNR shocks. In this contribution, I will review the current status of the SNR paradigm for the origin of cosmic rays, highlighting how (current and future) gamma-ray and neutrino observations can contribute to test this scenario and possibly provide constraints to model parameters. At the same time, I will also discuss how some features in the cosmic-ray spectrum are possibly related to run-away particles injected by SNRs in the Galaxy, and what information do they provide about these sources.