A ``skein relation'' can be viewed as a linear relation satisfied by the
R-matrix for a quantum group; one of the first uses of skein relations was
to give a combinatorial construction of Reshetikhin-Turaev invariants of
knots in S^3. The Hall algebra of an abelian (or triangulated) category
"counts extensions" in the category. We briefly describe how skein relations
appear in the Hall algebra of coherent sheaves of an elliptic curve, the
Hall algebra of the Fukaya category of a surface, and factorization homology
of a surface. No familiarity with the objects mentioned above will be
assumed for the talk.