  We give a brief review of the origin and acceleration of cosmic rays (CRs),
emphasizing the production of CRs at different stages of supernova evolution by
the first-order Fermi shock acceleration mechanism. We suggest that supernovae
with trans-relativistic outflows, despite being rather rare, may accelerate CRs
to energies above 10$^{18}$ eV over the first year of their evolution.
Supernovae in young compact clusters of massive stars, and interaction powered
superluminous supernovae, may accelerate CRs well above the PeV regime. We
discuss the acceleration of the bulk of the galactic CRs in isolated supernova
remnants and re-acceleration of escaped CRs by the multiple shocks present in
superbubbles produced by associations of OB stars. The effects of magnetic
field amplification by CR driven instabilities, as well as superdiffusive CR
transport, are discussed for nonthermal radiation produced by nonlinear shocks
of all speeds including trans-relativistic ones.
