Knowledge graphs (KGs) represent facts in the form of subject-predicate-object triples and are widely used to represent and share knowledge on the Web. Their ability to represent data in complex domains augmented with semantic annotations has attracted the attention of both research and industry. Yet, their widespread adoption in various domains and their generation processes have made the contents of these resources complicated. We speak of knowledge graph exploration as of the gradual discovery and understanding of the contents of a large and unfamiliar KG. In this paper, we present an overview of the state-of-the-art approaches for KG exploration. We divide them into three areas: profiling, search, and analysis and we argue that, while KG profiling and KG exploratory search received considerable attention, exploratory KG analytics is still in its infancy. We conclude with an overview of promising future research directions towards the design of more advanced KG exploration techniques.