Fog computing has emerged as a prospective paradigm to address the computational requirements of IoT applications, extending the capabilities of cloud computing to the network edge. Task scheduling is pivotal in enhancing energy efficiency, optimizing resource utilization and ensuring the timely execution of tasks within fog computing environments. This article presents a comprehensive review of the advancements in task scheduling methodologies for fog computing systems, covering priority-based, greedy heuristics, metaheuristics, learning-based, hybrid heuristics, and nature-inspired heuristic approaches. Through a systematic analysis of relevant literature, we highlight the strengths and limitations of each approach and identify key challenges facing fog computing task scheduling, including dynamic environments, heterogeneity, scalability, resource constraints, security concerns, and algorithm transparency. Furthermore, we propose future research directions to address these challenges, including the integration of machine learning techniques for real-time adaptation, leveraging federated learning for collaborative scheduling, developing resource-aware and energy-efficient algorithms, incorporating security-aware techniques, and advancing explainable AI methodologies. By addressing these challenges and pursuing these research directions, we aim to facilitate the development of more robust, adaptable, and efficient task-scheduling solutions for fog computing environments, ultimately fostering trust, security, and sustainability in fog computing systems and facilitating their widespread adoption across diverse applications and domains.