Since the late '50s, when the first artificial satellite was launched, the number of resident space objects (RSOs) has steadily increased. It is estimated that around 1 Million objects larger than 1 cm are currently orbiting the Earth, with only 30,000, larger than 10 cm, presently being tracked. To avert a chain reaction of collisions, termed Kessler Syndrome, it is indispensable to accurately track and predict space debris and satellites' orbit alike. Current physics-based methods have errors in the order of kilometres for 7 days predictions, which is insufficient when considering space debris that have mostly less than 1 meter. Typically, this failure is due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, as well as specific unknown characteristics such as mass or geometry of the RSO. Leveraging data-driven techniques, namely machine learning, the orbit prediction accuracy can be enhanced: by deriving unmeasured objects' characteristics, improving non-conservative forces' effects, and by the superior abstraction capacity that Deep Learning models have of modelling highly complex non-linear systems. In this survey, we provide an overview of the current work being done in this field.