  We present quantities which characterize the sensitivity of
gravitational-wave observatories to sources at cosmological distances. In
particular, we introduce and generalize the horizon, range, response, and reach
distances. These quantities incorporate a number of important effects,
including cosmologically well-defined distances and volumes, cosmological
redshift, cosmological time dilation, and rate density evolution. In addition,
these quantities incorporate unique aspects of gravitational wave detectors,
such as the variable sky sensitivity of the detectors and the scaling of the
sensitivity with inverse distance. An online calculator
(https://users.rcc.uchicago.edu/~dholz/gwc/) and python notebook
(https://github.com/hsinyuc/distancetool) to determine GW distances are
available. We provide answers to the question: "How far can gravitational-wave
detectors hear?"
