In this thesis, I construct and evaluate biophysically realistic mathematical models of potassium transport in two inner ear epithelia. Deficits in potassium transport cause deafness and imbalance, because proper hearing and balance require the presence of an electrochemical potassium gradient. The first tissue considered is the cochlear stria vascularis, which produces the high endolymphatic potassium and endocochlear potential (EP). The prevailing theory for the operation of this epithelium is that one layer of cells provides a large current, which creates a low intrastrial potassium concentration that allows the EP to develop across the membranes of a second layer. The second tissue is the vestibular sensory epithelium, in which local ion accumulation in calyx-type synapses has been proposed to enhance synaptic signaling. I use computational models to study the behavior of both systems. For the stria vascularis, I applied compartmental analysis with the addition of equations for volume and electrical potentials. For the calyx synapse, I derive a distributed circuit model with Nernst-Planck electrodiffusion of potassium and a stochastic description of quantal transmission. Both models are based upon experimentally derived channel and transporter kinetics. The model of the stria vascularis accurately reproduces experimental measurements and confirms that the two-layer theory of EP generation is feasible with known channels and transporters. I can also estimate the potassium in the intrastrial space, which has not been accurately measured. Using the calyx model, I demonstrate nonquantal transmission in spite of high transporter densities, primarily by potassium accumulation and in a small part by ephaptic transmission. In addition to a direct effect on the afferent neuron, potassium increases the effective input resistance of the model hair cell, increasing quantal release. The model also exhibits retrograde transmission of afferent action potentials, which may be an observable measure of ephaptic transmission. These models provide information about variables that cannot easily be measured, such as the intrastrial and calyceal cleft potassium concentrations. Over time this work could grow into a complete multiscale model of inner ear ion transport, allowing virtual experiments of loss of function and restorative therapies.