Abstract : Mobile Edge Computing (MEC) has emerged as a disruptive paradigm for supporting computation intensive and latency critical applications on resource constrained mobile devices. By offloading tasks to proximate edge servers, MEC reduces communication delay and energy consumption compared to conventional cloud computing. However, dynamic radio access conditions, heterogeneous server capacities, and user mobility make efficient task offloading highly challenging. Recent advances in deep learning provide promising alternatives by enabling adaptive, data driven decision making. This survey presents a comprehensive review of deep learning approaches for MEC task offloading. A novel dual taxonomy is proposed, jointly classifying existing works by learning methodology—supervised, unsupervised, reinforcement, and distributed learning—and by optimization objectives including deadline satisfaction, energy efficiency, cost reduction, and scalability. Representative neural architectures such as multilayer perceptrons, convolutional networks, recurrent models, and reinforcement learning agents are analyzed for their suitability in dynamic MEC environments. Distributed learning paradigms including federated and split learning are further examined to highlight privacy preserving and scalable edge intelligence. Key lessons and limitations are distilled, emphasizing the strengths of deep learning in feature extraction, data driven modeling, online adaptation, and distributed coordination, while acknowledging challenges such as training complexity, lack of transparency, and communication overhead. Finally, future research directions are outlined, including hybrid optimization frameworks, adaptive federated learning, explainable AI, sustainable edge intelligence, transformer based architectures, multi agent reinforcement learning, and emerging applications such as vehicular edge computing and IoT driven smart cities. By explicitly highlighting novelty and providing a forward looking roadmap, this survey advances the state of knowledge in deep learning enabled MEC offloading and serves as both a reference for established scholars and a guide for new researchers entering the field.