Task scheduling in mobile cloud computing is a key research area that focuses on efficiently assigning computational tasks from mobile devices to cloud, edge, or fog resources to optimize performance, energy consumption, and Quality of Service (QoS). Research papers in this domain explore static, dynamic, and adaptive scheduling strategies that consider heterogeneous device capabilities, varying workloads, latency constraints, network conditions, and energy efficiency requirements. Studies highlight the use of heuristic algorithms, metaheuristic approaches, optimization models, and machine learning techniques—including reinforcement learning and deep learning—for intelligent and context-aware task scheduling. Recent works also investigate multi-tier mobile cloud environments, where edge, fog, and cloud layers collaborate to improve scalability, fault tolerance, and service continuity. Security- and privacy-aware scheduling frameworks are increasingly incorporated to ensure sensitive data is protected during task migration. Applications include smart healthcare, autonomous vehicles, industrial IoT, augmented/virtual reality, and mobile multimedia services. Overall, research in task scheduling for mobile cloud computing enables adaptive, efficient, and secure execution of distributed workloads, balancing performance, energy consumption, and resource utilization in dynamic mobile environments.