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With the evolution of 5G and Internet of Things technologies, Mobile Edge Computing (MEC) has emerged as a major computing paradigm. Compared to cloud computing, MEC integrates network control, computing, and storage to customizable, fast, reliable, and secure distributed services that are closer to the user and data site. Although a popular research topic, MEC resource management comes in many forms due to its emerging nature and there exists little consensus in the community. In this survey, we present a comprehensive review of existing research problems and relevant solutions within MEC resource management. We first describe the major problems in MEC resource allocation when the user applications have diverse performance requirements. We discuss the unique challenges caused by the dynamic nature of the environments and use cases where MEC is adopted. We also explore and categorize existing solutions that address such challenges. We particularly explore traditional optimization-based methods and deep learning-based approaches. In addition, we take a deeper dive into the most popular applications and use cases that adopt MEC paradigm and how MEC provides customized solutions for each use cases, in particular, video analytics applications. Finally, we outline the open research challenges and future directions. 1