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In recent years, the research on reinforcement learning (RL) has focused on function approximation in learning prediction and control of Markov decision processes (MDPs). The usage of function approximation techniques in RL will be essential to deal with MDPs with large or continuous state and action spaces. In this paper, a comprehensive survey is given on recent developments in RL algorithms with function approximation. From a theoretical point of view, the convergence and feature representation of RL algorithms are analyzed. From an empirical aspect, the performance of different RL algorithms was evaluated and compared in several benchmark learning prediction and learning control tasks. The applications of RL with function approximation are also discussed. At last, future works on RL with function approximation are suggested.