Computing demand in cloud environments has grown exponentially over the past decade, due to the increase in cloud workload related to new services such as artificial intelligence, autonomous vehicles, augmented reality, etc. As a result, the ICT sector has seen its carbon emissions increase. It is possible to adopt less energy-intensive strategies and consume electricity produced by renewable energy to limit the increase in carbon emissions. In this article, we present a review of the workload-shifting techniques available for sustainable workload deployment, providing an innovative framework that can be used to analyze energy-aware approaches that apply any type of shifting technique. We identified three main concepts: compute a workload at a different time, deploy a workload and/or its data in a different location, or use alternative processing to provide a good-enough option for a workload. A definition and some examples are given for each shifting concept, and then we explore the opportunities and challenges of combining different shifting techniques.