The finiteness of black hole entropy suggest that spacetime is fundamentally
discrete, and hints at an underlying relationship between geometry and
"information". The foundation of this relationship is yet to be uncovered, but
should manifest itself in a theory of quantum gravity. We review recent
attempts to define a microscopic measure for black hole entropy and for the
maximum entropy of spherically symmetric spacelike regions, within the causal
set approach to quantum gravity.Comment: 5 pages, 1 figure. Talk given by S. Zohren at the Eleventh Marcel
Grossmann Meeting on General Relativity at the Freie U. Berlin, July 23 - 29,
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