Proteolytic processing of Gag and Gag-Pol polyproteins by the viral protease (PR) is crucial for the production of infectious HIV-1, and inhibitors of the viral PR are an integral part of current antiretroviral therapy. The process has several layers of complexity (multiple cleavage sites and substrates, multiple enzyme forms, PR auto-processing), which calls for a systems level approach to identify key vulnerabilities and optimal treatment strategies. Here we present the first full reaction kinetics model of proteolytic processing by HIV-1 PR, taking into account all canonical cleavage sites within Gag and Gag-Pol, intermediate products and enzyme forms, enzyme dimerization, the initial auto-cleavage of full-length Gag-Pol as well as self-cleavage of PR. The model allows us to identify the rate limiting step of virion maturation and the parameters with the strongest effect on maturation kinetics. Using the modelling framework, we predict interactions and compensatory potential between individual cleavage rates and drugs, characterize the time course of the process, explain the steep dose response curves associated with PR inhibitors and gain new insights into drug action. While the results of the model are subject to limitations arising from the simplifying assumptions used and from the uncertainties in the parameter estimates, the developed framework provides an extendable open-access platform to incorporate new data and hypotheses in the future.