A convolutional neural network (CNN) is one of the most significant networks in the deep learning field. Since CNN made impressive achievements in many areas, including but not limited to computer vision and natural language processing, it attracted much attention from both industry and academia in the past few years. The existing reviews mainly focus on CNN's applications in different scenarios without considering CNN from a general perspective, and some novel ideas proposed recently are not covered. In this review, we aim to provide some novel ideas and prospects in this fast-growing field. Besides, not only 2-D convolution but also 1-D and multidimensional ones are involved. First, this review introduces the history of CNN. Second, we provide an overview of various convolutions. Third, some classic and advanced CNN models are introduced; especially those key points making them reach state-of-the-art results. Fourth, through experimental analysis, we draw some conclusions and provide several rules of thumb for functions and hyperparameter selection. Fifth, the applications of 1-D, 2-D, and multidimensional convolution are covered. Finally, some open issues and promising directions for CNN are discussed as guidelines for future work.