Rift Valley fever (RVF) is a zoonotic arbovirosis which has been reported across Africa including the northernmost edge, South West Indian Ocean islands, and the Arabian Peninsula. The virus is responsible for high abortion rates and mortality in young ruminants, with economic impacts in affected countries. To this day, RVF epidemiological mechanisms are not fully understood, due to the multiplicity of implicated vertebrate hosts, vectors and ecosystems. In this context, mathematical models are useful tools to develop our understanding of complex systems, and mechanistic models are particularly suited to data-scarce settings. In this work, we performed a systematic review of mechanistic models studying RVF, to explore their diversity and their contribution to the understanding of this disease epidemiology. Researching Pubmed and Scopus databases (October 2021), we eventually selected 48 papers, which needed to provide a clear description of a mechanistic model with numerical application to RVF. We categorized models as theoretical, applied or grey, according to their will to represent a specific geographical context and their use of data to fulfill this intention. We discussed their contributions to the understanding of RVF epidemiology, and highlighted that theoretical and applied models can use different tools to meet common objectives. Through the examination of model features, we identified research questions left unexplored across scales, along with a substantial lack of justification when choosing a functional form for the force of infection. Overall, we showed a great diversity in RVF models, leading to substantial progress in our comprehension of epidemiological mechanisms. To go further, data gaps must be fulfilled, and modelers need to go the extra mile regarding transparency.