 Perhaps the best-known proposal for a hypercomputer is due to Mark Hogarth (1994, 2004), who developed an idea of Itamar Pitowsky (1990). Relativistic hypercomputers exploit the properties of a special kind of spacetime called Malament-Hogarth spacetime, which is physically possible in the sense of constituting a solution to Einstein’s field equations for General Relativity. Malament-Hogarth spacetimes contain regions with an infinite time-like trajectory λ that can be circumvented by a finite time-like trajectory γ. In other words, λ and γ have a common origin, and there is a spacetime point p on γ such that λ, even though it is infinite, lies entirely in p’s chronological past. If an observer launches a TM along λ and then travels along γ she may, within finite time, find herself in the future of an infinitely long computation performed by the TM. If the TM is able to send signals to the observer, the observer would be able to know the outcome of a potentially infinitely long computation, thereby having computational means more powerful than (ordinary) TMs. For instance, an observer may be able to obtain the results of an arbitrary instance of the halting function for TMs.