In this paper, we present a survey of deep learning-based methods for the regression of gaze direction vector from head and eye images. We describe in detail numerous published methods with a focus on the input data, architecture of the model, and loss function used to supervise the model. Additionally, we present a list of datasets that can be used to train and evaluate gaze direction regression methods. Furthermore, we noticed that the results reported in the literature are often not comparable one to another due to differences in the validation or even test subsets used. To address this problem, we re-evaluated several methods on the commonly used in-the-wild Gaze360 dataset using the same validation setup. The experimental results show that the latest methods, although claiming state-of-the-art results, significantly underperform compared with some older methods. Finally, we show that the temporal models outperform the static models under static test conditions.