Carbon aware scheduling is a technique used to optimize the allocation of compute resources in a cloud computing system in order to minimize the carbon emissions associated with running those resources. As the demand for computing resources continues to grow, the carbon emissions associated with data centers and other computing infrastructure are becoming an increasingly significant contributor to climate change. In this paper, we present an overview of the state of the art in carbon aware scheduling techniques for cloud computing systems, including both centralized and decentralized approaches. We discuss the advantages and disadvantages of different carbon aware scheduling approaches, and provide insights into the trade-offs that need to be considered when choosing an approach. Finally, we identify key challenges and open problems in the field of carbon aware scheduling for cloud computing systems, and suggest directions for future research.