Since the 1970s, computational modeling has been used to investigate the fundamental mechanisms of cochlear implant stimulation. Lumped parameter models and analytical models have been used to simulate cochlear potentials, as well as three-dimensional volume conduction models based on the Finite Difference, Finite Element, and Boundary Element methods. Additionally, in order to simulate neural responses, several of these cochlear models have been combined with nerve models, which were either simple activation functions or active nerve fiber models of the cochlear auditory neurons. This review paper will present an overview of the ways in which these computational models have been employed to study different stimulation strategies and electrode designs. Research into stimulation strategies has concentrated mainly on multipolar stimulation as a means of achieving current focussing and current steering, while modeling work on electrode design has been chiefly concerned with finding the optimal position and insertion depth of the electrode array. Finally, the present and future of computational modeling of the electrically stimulated cochlea is discussed.