  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.
