Incorporating the Internet of Things (IoT) with cloud computing has significantly changed various industries and improved the quality of life. Despite these advantages, cloud computing is not enough for real-time applications due to the dynamic nature of IoT Devices (IoTDs) and their unpredictable locations, heterogeneity constraints, fault sensitivity, and power supply limitations. Accordingly, Cisco has introduced fog computing as a solution that relocates computation to the network’s edge. This article presents a Systematic Literature Review (SLR) of 109 research articles published between 2016 and 2023 on modern fog resource management approaches. Based on a comprehensive taxonomy, these approaches are classified and compared considering several technological benchmarks, including Quality of Service (QoS) parameters, algorithms, techniques, evaluation methods, case studies, and their strengths, limitations, and novel findings. Additionally, a separate section extensively discusses future trends and open issues in fog computing resource management. In this study, security issues are not addressed, which is suggested for future studies.