In this paper, we propose an elegant solution that is directly addressing the bottlenecks of the traditional deep learning approaches and offers an explainable internal architecture that can outperform the existing methods, requires very little computational resources (no need for GPUs) and short training times (in the order of seconds). The proposed approach, xDNN is using prototypes. Prototypes are actual training data samples (images), which are local peaks of the empirical data distribution called typicality as well as of the data density. This generative model is identified in a closed form and equates to the pdf but is derived automatically and entirely from the training data with no user- or problem-specific thresholds, parameters or intervention. The proposed xDNN offers a new deep learning architecture that combines reasoning and learning in a synergy. It is non-iterative and non-parametric, which explains its efficiency in terms of time and computational resources. From the user perspective, the proposed approach is clearly understandable to human users. We tested it on challenging problems as the classification of different lighting conditions for driving scenes (iROADS), object detection (Caltech-256, and Caltech-101), and SARS-CoV-2 identification via computed tomography scan (COVID CT-scans dataset). xDNN outperforms the other methods including deep learning in terms of accuracy, time to train and offers an explainable classifier.