The invention of heat pipe solar collectors (HPSCs) is considered as an immense step forward towards solving the challenges of conventional solar thermal systems. Their unique qualities have acted as a great motivation for researchers to focus their studies on HPSCs and their applications. A considerable share of these studies has been allocated to theoretical studies due to several technical and economic reasons. However, to the authors' knowledge and despite many valuable efforts in this field, there is no review paper available to summarise the relevant proposed and developed theoretical models to date and identifies the research gaps in this field. Therefore, in this review paper, the latest theoretical studies in the field of HPSCs along with their advantages, disadvantages, and contribution have been categorized, reviewed, and discussed. First, the operational principles and structure of HPSCs have been explained to create a background for readers. This is followed by a short section dedicated to the simulation of solar radiation as the most important input for all solar mathematical models. In addition, various mathematical approaches including steady state models (i.e. one-dimensional energy balance and thermal resistance network methods), dynamic models, and models for novel configurations and applications of HPSCs have been reviewed. Moreover, mathematical models to determine the exergy efficiency of HPSCs, which is an effective tool to evaluate the solar systems from a thermodynamic point of view, have been presented. Finally, the challenges, research gaps, and recommendations for future research directions have been provided.