This talk will introduce the notion of a factorization algebra, which offers a simultaneous generalization of several constructions, including associative algebras, vertex algebras, and cosheaves. Beilinson and Drinfeld developed factorization algebras to capture the structure of chiral conformal field theory, but it has been found to apply more broadly to field theories in Riemannian signature. I will survey why the observables of a perturbative field theory form a factorization algebra and what that buys you, while keeping higher algebraic technicalities to a minimum. Along the way I will mention several concrete examples, from ordinary mechanics to 4-dimensional gauge theories.