The energy consumption of Cloud–Edge systems is becoming a critical concern economically, environmentally, and societally; some studies suggest data centers and networks will collectively consume 18% of global electrical power by 2030. New methods are needed to mitigate this consumption, e.g. energy-aware workload scheduling, improved usage of renewable energy sources, etc. These schemes need to understand the interaction between energy considerations and Cloud–Edge components. Model-based approaches are an effective way to do this; however, current theoretical Cloud–Edge models are limited, and few consider energy factors. This paper analyses all relevant models proposed between 2016 and 2023, discovers key omissions, and identifies the major energy considerations that need to be addressed for Green Cloud–Edge systems (including interaction with energy providers). We investigate how these can be integrated into existing and aggregated models, and conclude with the high-level architecture of our proposed solution to integrate energy and Cloud–Edge models together.