Machine learning (ML) is the branch of computer science that studies computer algorithms that can learn from data. It is mainly divided into supervised learning, where the computer is presented with examples of entries, and the goal is to learn a general rule that maps inputs to outputs, and unsupervised learning, where no label is provided to the learning algorithm, leaving it alone to find structures. Deep learning is a branch of machine learning based on numerous layers of artificial neural networks, which are computing systems inspired by the biological neural networks that constitute animal brains. In asteroid dynamics, machine learning methods have been recently used to identify members of asteroid families, small bodies images in astronomical fields, and to identify resonant arguments images of asteroids in three-body resonances, among other applications. Here, we will conduct a full review of available literature in the field and classify it in terms of metrics recently used by other authors to assess the state of the art of applications of machine learning in other astronomical subfields. For comparison, applications of machine learning to Solar System bodies, a larger area that includes imaging and spectrophotometry of small bodies, have already reached a state classified as progressing. Research communities and methodologies are more established, and the use of ML led to the discovery of new celestial objects or features, or new insights in the area. ML applied to asteroid dynamics, however, is still in the emerging phase, with smaller groups, methodologies still not well-established, and fewer papers producing discoveries or insights. Large observational surveys, like those conducted at the Zwicky Transient Facility or at the Vera C. Rubin Observatory, will produce in the next years very substantial datasets of orbital and physical properties for asteroids. Applications of ML for clustering, image identification, and anomaly detection, among others, are currently being developed and are expected of being of great help in the next few years.
