 In order to present some central logics of conditionals based on the possible-worlds framework, we adopt a Frege-Hilbert axiomatic perspective and introduce a list of axioms and rules of inference. Our presentation and choice of terminology relies on Nute (1980) as well as Herzig (1996), Unterhuber and Schurz (2014), and Crupi and Iacona (forthcoming-b).