Mobile edge computing (MEC) deploys storage and computing resources in the proximity of end devices. With MEC, the data generated by end devices can be offloaded to the edge servers for processing, rather than sending them to the remote cloud servers. As a result, the service latency can be greatly improved and the network congestion can be mitigated. In this chapter, we investigate computation offloading in a dynamic MEC system with multiple cooperative edge servers, where computational tasks with various requirements are dynamically generated by end devices and offloaded to MEC servers in a time-varying operating environment (e.g., wireless channel condition and workloads of the edge servers change over time). The objective is to maximize the number of completed tasks before their respective required deadlines and minimize the energy consumption. To this end, this chapter presents an end-to-end Deep Reinforcement Learning (DRL) approach to select the best edge server for offloading and allocate the optimal computational resource such that the expected long-term utility is maximized. The simulation results are provided to evaluate the performance of this DRL approach.