Neural-symbolic computing (NeSy), which pursues the integration of the symbolic and statistical paradigms of cognition, has been an active research area of Artificial Intelligence (AI) for many years. As NeSy shows promise of reconciling the advantages of reasoning and interpretability of symbolic representation and robust learning in neural networks, it may serve as a catalyst for the next generation of AI. In the present paper, we provide a systematic overview of the recent developments and important contributions of NeSy research. Firstly, we introduce study history of this area, covering early work and foundations. We further discuss background concepts and identify key driving factors behind the development of NeSy. Afterward, we categorize recent landmark approaches along several main characteristics that underline this research paradigm, including neural-symbolic integration, knowledge representation, knowledge embedding, and functionality. Next, we briefly discuss the successful application of modern NeSy approaches in several domains. Then, we benchmark several NeSy methods on three representative application tasks. Finally, we identify the open problems together with potential future research directions. This survey is expected to help new researchers enter this rapidly evolving field and accelerate the progress towards data-and knowledge-driven AI.