  Understanding the origins of ultrahigh energy cosmic rays (UHECRs) - which
reach energies in excess of $10^{20}~{\rm eV}$ - stretches particle
acceleration physics to its very limits. In this review, we discuss how such
energies can be reached, using general arguments that can often be derived on
the back of an envelope. We explore possible particle acceleration mechanisms,
with special attention paid to shock acceleration. Informed by the arguments
derived, we discuss where UHECRs might come from and which classes of powerful
astrophysical objects could be UHECR sources; generally, we favour radio
galaxies, GRB afterglows and other sources which are not too compact and
dissipate prodigious amounts of energy on large scales, allowing them to
generate large products $\beta B R$ without the CRs undergoing restrictive
losses. Finally, we discuss when UHECRs are accelerated by highlighting the
importance of source variability, and explore the intriguing possibility that
the UHECR arrival directions are partly a result of "echoes" from magnetic
structures in the local Universe.
