Reliable uncertainty estimation has become a crucial requirement for the industrial deployment of deep learning algorithms, particularly in high-risk applications such as autonomous driving and medical diagnosis. However, uncertainty estimation methods relying on deep ensembling or Bayesian neural networks typically entail significant computational overhead. To address this challenge, a novel paradigm called Evidential Deep Learning (EDL) has emerged, providing high-quality uncertainty estimation with minimal additional computation in a single forward pass. This survey provides a comprehensive overview of the current research on EDL, designed to offer readers a broad introduction to the field without assuming prior knowledge. Specifically, we first delve into the theoretical foundation of EDL, the subjective logic theory, and discuss its distinctions from other uncertainty estimation frameworks. We further present existing theoretical advancements in EDL from four perspectives: reformulating the evidence collection process, improving uncertainty estimation via OOD samples, delving into various training strategies, and evidential regression networks. Thereafter, we elaborate on its extensive applications across various machine learning paradigms and downstream tasks. In the end, an outlook on future directions for better performances and broader adoption of EDL is provided, highlighting potential research avenues.