Smart grid and cloud computing architectures have been perfectly suiting each other naturally. As a result, over the years cloud computing architectures have dominated the implementations of smart grid applications to address computing needs. However, due to continuing additions of heterogeneous (sensing and actuating) devices, emergence of Internet of Things (IoT), and massive amount of data collected across the grids for analytics, have contributed to the complexity of smart grids, making cloud computing architectures no longer suitable to provide smart grid services effectively. Edge and Fog computing approaches have relieved the cloud computing architectures of problems related to network congestion, latency and locality by shift of control, intelligence and trust to the edge of the network. In this paper, a systematic literature review is used to explore the research trend of the actual implementations of edge and fog computing for smart grid applications. A total of 70 papers were reviewed from the popular digital repositories. The study has revealed that, there is significant increase in the number of smart grid applications that have exploited the use edge and fog computing approaches. The study also shows that, considerable number of the smart grid applications are related to energy optimizations and intelligent coordination of smart grid resources. There are also challenges and issues that hinder smooth adoption of edge and fog computing for smart grid applications, which include security, interoperability and programming models.