Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more data or refining the learning models. Over the last few years, scholars have proposed many epistemic uncertainty handling techniques which can be roughly grouped into two categories, i.e., Bayesian and ensemble. This paper provides a comprehensive review of epistemic uncertainty learning techniques in supervised learning over the last five years. As such, we, first, decompose the epistemic uncertainty into bias and variance terms. Then, a hierarchical categorization of epistemic uncertainty learning techniques along with their representative models is introduced. In addition, several applications such as computer vision (CV) and natural language processing (NLP) are presented, followed by a discussion on research gaps and possible future research directions.