Recently, neural network-based deep learning methods have been popularly applied to computer vision, speech signal processing and other pattern recognition areas. Remarkable success has been demonstrated by using the deep learning approaches. The purpose of this article is to provide a comprehensive survey for the neural network-based deep learning approaches on acoustic event detection. Different deep learning-based acoustic event detection approaches are investigated with an emphasis on both strongly labeled and weakly labeled acoustic event detection systems. This paper also discusses how deep learning methods benefit the acoustic event detection task and the potential issues that need to be addressed for prospective real-world scenarios.