  Factorization algebras are local-to-global objects living on manifolds, and
they arise naturally in mathematics and physics. Their local structure
encompasses examples like associative algebras and vertex algebras; in these
examples, their global structure encompasses Hochschild homology and conformal
blocks. In the setting of quantum field theory, factorization algebras
articulate a minimal set of axioms satisfied by the observables of a theory,
and they capture concepts like the operator product and correlation functions.
In this survey article for the Encyclopedia of Mathematical Physics, 2nd
Edition, we give the definitions and key examples, compare this approach with
other approaches to mathematically formalizing field theory, describe key
results, and explain how higher symmetries can be encoded in this framework.
