Ontology learning, particularly axiom learning, is a challenging task that focuses on building expressive and decidable ontologies. The literature proposes several research efforts aimed to resolve the complexities inherent in axiom and rule learning, which seeks to automatically infer logical constructs from diverse data sources. The goal of this paper is to conduct a comprehensive review of existing work in this domain. It aims to critically analyze the contributions and limitations of current approaches, providing a clear understanding of the state-of-the-art and identifying areas where further research is needed.