This article contains all of the information needed to conduct a study on monocular facial depth estimation problems. A brief literature review and applications on facial depth map research were offered first, followed by a comprehensive evaluation of publicly available facial depth datasets and widely used loss functions. The key properties and characteristics of each facial depth map dataset are described and evaluated. Furthermore, facial depth maps loss functions are briefly discussed, which will make it easier to train neural facial depth models on a variety of datasets for both short-and long-range depth maps. The network's design and components are essential, but its effectiveness is largely determined by how it is trained, which necessitates a large dataset and a suitable loss function. Implementation details of how neural depth networks work and their corresponding evaluation matrices are presented and explained. In addition, an SoA neural model for facial depth estimation is proposed, along with a detailed comparison evaluation and, where feasible, direct comparison of facial depth estimation methods to serve as a foundation for a proposed model that is utilized. The model employed shows better performance compared with current state-of-the-art methods when tested across four datasets. The new loss function used in the proposed method helps the network to learn the facial regions resulting in an accurate depth prediction. The network is trained on synthetic human facial depth datasets whereas for validation purposes real as well as synthetic facial images are used. The results prove that the trained network outperforms current state-of-the-art networks performances, thus setting up a new baseline method for facial depth estimations.