In recent years, Antiretroviral Therapy (ART) has become commonplace for treating HIV infections, although a cure remains elusive, given reservoirs of replicating latently-infected cells, which are resistant to normal treatment regimes. Treatment interruptions, whether ad hoc or structured, are known to cause a rapid increase in viral production to detectable levels, but numerous clinical trials remain inconclusive on the dangers inherent in this resurgence. In consequence, interest in examining interruption strategies has recently been rekindled. This overview considers modelling approaches, which have been used to explore the issue of treatment interruption. We highlight their purpose and the formalisms employed and examine ways in which clinical data have been used. Implementation of selected models is demonstrated, illustrative examples provided and model performance compared for these cases. Possible extensions to bottom-up modelling techniques for treatment interruptions are briefly discussed.