The rate at which matter flows into a galactic nucleus during early phases of galaxy evolution can sometimes exceed the Eddington limit of the growing central black hole by several orders of magnitude. We discuss the necessary conditions for the black hole to actually accrete this matter at such a high rate, and consider the observational appearance and detectability of a hyperaccreting black hole. In order to be accreted at a hyper-Eddington rate, the infalling gas must have a sufficiently low angular momentum. Although most of the gas is accreted, a significant fraction accumulates in an optically thick envelope with luminosity $\sim L_{\rm Edd}$, probably pierced by jets of much higher power. If $\dot M > 10^3 \dot M_{\rm Edd}$, the envelope spectrum resembles a blackbody with a temperature of a few thousand K, but for lower (but still hyper-Eddington) accretion rates the spectrum becomes a very dilute and hard Wien spectrum. We consider the likelihood of various regimes of hyperaccretion, and discuss its possible observational signatures.