There exist three mathematical formalizations of the concept of chiral conformal field theory: Vertex operator algebras, Conformal nets, and Segal CFTs. These three notions are expected/conjectured to be equivalent (provided appropriate qualifiers are added). In this overview talk, I will explain, based on examples, what are Vertex operator algebras, Conformal nets, and Segal CFTs. I will describe how one is supposed to go from one formalism to the other, and where the main difficulties lie.