Resource management in computing is a very challenging problem that involves making sequential decisions. Resource limitations, resource heterogeneity, dynamic and diverse nature of workload, and the unpredictability of fog/edge computing environments have made resource management even more challenging to be considered in the fog landscape. Recently Artificial Intelligence (AI) and Machine Learning (ML) based solutions are adopted to solve this problem. AI/ML methods with the capability to make sequential decisions like reinforcement learning seem most promising for these type of problems. But these algorithms come with their own challenges such as high variance, explainability, and online training. The continuously changing fog/edge environment dynamics require solutions that learn online, adopting changing computing environment. In this paper, we used standard review methodology to conduct this Systematic Literature Review (SLR) to analyze the role of AI/ML algorithms and the challenges in the applicability of these algorithms for resource management in fog/edge computing environments. Further, various machine learning, deep learning and reinforcement learning techniques for edge AI management have been discussed. Furthermore, we have presented the background and current status of AI/ML-based Fog/Edge Computing. Moreover, a taxonomy of AI/ML-based resource management techniques for fog/edge computing has been proposed and compared the existing techniques based on the proposed taxonomy. Finally, open challenges and promising future research directions have been identified and discussed in the area of AI/ML-based fog/edge computing.