Millimeter-wave sensing using automotive radar imposes high requirements on the applied signal processing in order to obtain the necessary resolution for current imaging radar. High-resolution direction of arrival estimation is needed to achieve the desired spatial resolution, limited by the total antenna array aperture. This work gives an overview of the recent progress and work in the field of deep learning based direction of arrival estimation in the automotive radar context, i.e. using only a single measurement snapshot. Additionally, several deep learning models are compared and investigated with respect to their suitability for automotive angle estimation. The models are trained with model- and data-based approaches for data generation, including simulated scenarios as well as real measurement data from more than 400 automotive radar sensors. Finally, their performance is compared to several baseline angle estimation algorithms like the maximum-likelihood estimator. All results are discussed with respect to the estimation error, the resolution of closely spaced targets and the total estimation accuracy. The overall results demonstrate the viability and advantages of the proposed data generation methods, as well as super-resolution capabilities of several architectures.