A parabolic trough solar collector (PTSC) has proved itself in solar to thermal conversion and also in serving various applications as desalination, heat-intensive industrial processes, etc. Installing a PTSC to serve a particular application requires a large setup and capital, so, it is expected that they work at their maximum efficiency. Thus, the analysis pertaining to identifying the possibilities that can help to improve the PTSC efficiency becomes important. Modeling of PTSC serves as a good option to analyze and suggest viable improvements for it. To support the aforementioned, the current study focuses on providing details on several existing grey box modeling approaches for PTSC. It surveys and define a unique taxonomy of various approaches, thus, bringing a new perspective to the topic of research. The fundamentals of several modeling methodologies, as well as the associated investigations are exhibited. A synopsis of various components of PTSC is also provided.