Modern artificial intelligence provides a novel way of producing digital art in styles. The expressive power of neural networks enables the realm of visual style transfer methods, which can be used to edit images, videos, and 3D data to make them more artistic and diverse. This paper reports on recent advances in neural stylization for 3D data. We provide a taxonomy for neural stylization by considering several important design choices, including scene representation, guidance data, optimization strategies, and output styles. Building on such taxonomy, our survey first revisits the background of neural stylization on 2D images, and then provides in-depth discussions on recent neural stylization methods for 3D data, where we also provide a mini-benchmark on artistic stylization methods. Based on the insights gained from the survey, we then discuss open challenges, future research, and potential applications and impacts of neural stylization.