Cochlear implants electrically stimulate surviving auditory neurons in the cochlea to provide severely or profoundly deaf people with access to hearing. Signal processing strategies derive frequency-specific information from the acoustic signal and code amplitude changes in frequency bands onto amplitude changes of current pulses emitted by the tonotopically arranged intracochlear electrodes. This article first describes how parameters of the electrical stimulation influence the loudness evoked and then summarizes two different phenomenological models developed by McKay and colleagues that have been used (...) to explain psychophysical effects of stimulus parameters on loudness, detection, and modulation detection. The Temporal Model is applied to single-electrode stimuli and integrates cochlear neural excitation using a central temporal integration window analogous to that used in models of normal hearing. Perceptual decisions are made using decision criteria applied to the output of the integrator. By fitting the model parameters to a variety of psychophysical data, inferences can be made about how electrical stimulus parameters influence neural excitation in the cochlea. The Detailed Model is applied to multi-electrode stimuli, and includes effects of electrode interaction at a cochlear level and a transform between integrated excitation and specific loudness. The Practical Method of loudness estimation is a simplification of the Detailed Model and can be used to estimate the relative loudness of any multi-electrode pulsatile stimuli without the need to model excitation at the cochlear level. Clinical applications of these models to novel sound processing strategies are described. (shrink)