  Numerical simulations indicate that black holes carrying linear momentum
and/or orbital momentum can power jets. The jets extract the kinetic energy
stored in the black hole's motion. This could provide an important
electromagnetic counterpart to gravitational wave searches. We develop the
theory underlying these jets. In particular, we derive the analogues of the
Penrose process and the Blandford-Znajek jet power prediction for boosted black
holes. The jet power we find is $(v/2M)^2 \Phi^2/(4\pi)$, where $v$ is the
hole's velocity, $M$ is its mass, and $\Phi$ is the magnetic flux. We show that
energy extraction from boosted black holes is conceptually similar to energy
extraction from spinning black holes. However, we highlight two key technical
differences: in the boosted case, jet power is no longer defined with respect
to a Killing vector, and the relevant notion of black hole mass is observer
dependent. We derive a new version of the membrane paradigm in which the
membrane lives at infinity rather than the horizon and we show that this is
useful for interpreting jets from boosted black holes. Our jet power prediction
and the assumptions behind it can be tested with future numerical simulations.
