In recent years, the number of embedded computing devices connected to the Internet has exponentially increased. At the same time, new applications are becoming more complex and computationally demanding, which can be a problem for devices, especially when they are battery powered. In this context, the concepts of computation offloading and edge computing, which allow applications to be fully or partially offloaded and executed on servers close to the devices in the network, have arisen and received increasing attention. Then, the design of algorithms to make the decision of which applications or tasks should be offloaded, and where to execute them, is crucial. One of the options that has been gaining momentum lately is the use of Reinforcement Learning (RL) and, in particular, Deep Reinforcement Learning (DRL), which enables learning optimal or near-optimal offloading policies adapted to each particular scenario. Although the use of RL techniques to solve the computation offloading problem in edge systems has been covered by some surveys, it has been done in a limited way. For example, some surveys have analysed the use of RL to solve various networking problems, with computation offloading being one of them, but not the primary focus. Other surveys, on the other hand, have reviewed techniques to solve the computation offloading problem, being RL just one of the approaches considered. To the best of our knowledge, this is the first survey that specifically focuses on the use of RL and DRL techniques for computation offloading in edge computing system. We present a comprehensive and detailed survey, where we analyse and classify the research papers in terms of use cases, network and edge computing architectures, objectives, RL algorithms, decision-making approaches, and time-varying characteristics considered in the analysed scenarios. In particular, we include a series of tables to help researchers identify relevant papers based on specific features, and analyse which scenarios and techniques are most frequently considered in the literature. Finally, this survey identifies a number of research challenges, future directions and areas for further study.