Cochlear implants (CIs) restore audition to the profoundly deaf by directly stimulating the auditory nerve. For accurate speech perception, incoming sound must be encoded in a meaningful way, and transmitted along the auditory pathway. CIs encode speech by modulating the amplitude of pulse train sequences, this thesis investigates neural responses to amplitude modulated stimuli in the CI population. Envelope coding strategies facilitate a certain degree of speech perception in quiet conditions. However, performance rapidly degrades in adverse listening environments, and variability increases across users. The degradation and variability in performance is greater in the CI than acoustic hearing population. Less than a quarter of the variability between CI users can be explained by clinical factors. This thesis investigates the inter and intra subject variation in electrically evoked auditory steady-state responses (EASSRs). EASSRs are neural responses to repetitive auditory stimuli that can be measured using electroencephalography (EEG). EASSRs are used as a tool to probe the auditory system. The stimuli in this thesis consist of amplitude modulated pulse trains, which are designed to resemble clinical stimuli, yet allow each parameter to be carefully manipulated. In chapter 2, EASSRs to amplitude modulated stimuli are related to behavioural modulation sensitivity, a crucial metric for CI users. In chapter 3, the intra subject variability in EASSRs is investigated and related to speech perception in noise (SPIN). Investigation of neural processing in CI users has been hindered by incompatibilities with traditional analysis techniques such as magnetic resonance imaging (MRI). The permanent magnet, radio frequency (RF) transmission and electrical stimulation cause artifacts in the sensor measurements that obscures the desired signal. Additional signal processing is required to mitigate the effect of these artifacts. Chapter 4 develops an EEG methodology to determine where in the brain EASSRs are processed, this is used to demonstrate atypical auditory pathway activation in CI users. Chapter 5 introduces a real-time signal processing technique, which accounts for CI artifacts in EEG measurements, and reduces measurement time.