Cloud Computing is a well-established paradigm for building service-centric systems. However, ultra-low latency, high bandwidth, security, and real-time analytics are limitations in Cloud Computing when analysing and providing results for a large amount of data. Fog and Edge Computing offer solutions to the limitations of Cloud Computing. The number of agricultural domain applications that use the combination of Cloud, Fog, and Edge is increasing in the last few decades. This article aims to provide a systematic literature review of current works that have been done in Cloud, Fog, and Edge Computing applications in the smart agriculture domain between 2015 and up-to-date. The key objective of this review is to identify all relevant research on new computing paradigms with smart agriculture and propose a new architecture model with the combinations of Cloud–Fog–Edge. Furthermore, it also analyses and examines the agricultural application domains, research approaches, and the application of used combinations. Moreover, this survey discusses the components used in the architecture models and briefly explores the communication protocols used to interact from one layer to another. Finally, the challenges of smart agriculture and future research directions are briefly pointed out in this article.