Machine learning has achieved remarkable successes, yet its deployment in safety-critical domains remains hindered by an inherent inability to manage uncertainty, resulting in overconfident and unreliable predictions when models encounter out-of-distribution data, adversarial perturbations, or naturally fluctuating environments. This thesis, titled Epistemic Deep Learning: Enabling Machine Learning Models to 'Know When They Do Not Know', addresses these critical challenges by advancing the paradigm of Epistemic Artificial Intelligence, which explicitly models and quantifies epistemic uncertainty: the uncertainty arising from limited, biased, or incomplete training data, as opposed to the irreducible randomness of aleatoric uncertainty, thereby empowering models to acknowledge their limitations and refrain from overconfident decisions when uncertainty is high. Central to this work is the development of the Random-Set Neural Network (RS-NN), a novel methodology that leverages random set theory to predict belief functions over sets of classes, capturing the extent of epistemic uncertainty through the width of associated credal sets, applications of RS-NN, including its adaptation to Large Language Models (LLMs) and its deployment in weather classification for autonomous racing. In addition, the thesis proposes a unified evaluation framework for uncertainty-aware classifiers. Extensive experiments validate that integrating epistemic awareness into deep learning not only mitigates the risks associated with overconfident predictions but also lays the foundation for a paradigm shift in artificial intelligence, where the ability to 'know when it does not know' becomes a hallmark of robust and dependable systems. The title encapsulates the core philosophy of this work, emphasizing that true intelligence involves recognizing and managing the limits of one's own knowledge.