On Horizon Molecules and Entropy in Causal Sets

We review the different proposals and attempts to identify the “horizon molecules” that would give a kinematical estimation for the black hole entropy in causal set theory. The proposals are presented according to their chronological appearance in scientific literature. The review is neither very technical nor merely descriptive; it is aimed to provide the reader with a lucid introduction to the necessary concepts and mathematical background and give him or her a broad view on the subject, by focusing on the main technical and conceptual issues that summarize the progress made in the last two decades.