An algebraic structure is finitely related (has finite degree) if its term functions are determined
by some finite set of finitary relations. We show that the following finite semigroups are finitely
related: commutative semigroups, $3$-nilpotent monoids,
regular bands, semigroups with a single idempotent, and Clifford semigroups.
Further we provide the first example of a semigroup that is not finitely related: the 6-element
Brandt monoid. This answers a question by Davey, Jackson, Pitkethly, and Szabo.