Machine learning methods based on statistical principles have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. Traditional data models are mostly concerned with independent identically distributed data. The recent success of end-to-end modelling scheme using deep neural networks equipped with effective structures such as convolutional layers or skip connections allows the extension to more sophisticated and structured practical data, such as natural language, images, videos, etc. On the application side, vector fields are an extremely useful type of data in empirical sciences, as well as signal processing, e.g. non-parametric transformations of 3D point clouds using 3D vector fields, the modelling of the fluid flow in earth science, and the modelling of physical fields. This review article is dedicated to recent computational tools of vector fields, including vector data representations, predictive model of spatial data, as well as applications in computer vision, signal processing, and empirical sciences.
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