Relativistic gyrotrons (electron kinetic energy on the order of the rest energy or greater) differ from their weakly relativistic counterparts in two important ways: the Larmor radius is large, which puts bounds on the allowable pitch angle for a given beam tunnel radius and magnetic field, and operation at Doppler upshited frequencies, which allows for the extraction of energy from the axial motion, is feasible even in fast wave devices. Consequently, there are a number of issues that are not present at low voltage: computing the electromagnetic and AC space charge fields is not straightforward; achieving high efficiency while still maintaining the cutoff condition in the beam tunnels may be problematic, especially at cyclotron harmonics; and the use of slow wave structures to achieve very high electronic efficiency is a possibility. In this paper we consider how these issues affect modeling, and discuss the advantages and limitations of high voltage operation. We also present a specific example, the gyrotwistron, as a highly efficient device for operation in the high power regime.