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

How, where and when do cosmic rays reach ultrahigh energies?