The classic PBW theorem compares the universal enveloping algebra U(L) of a finite dimensional Lie algebra L to S(L), Â the symmetric algebra on L. The theorem is attributed to Poincare (1900) and Birkhoff-Will (1937). Many generalizations of the PBW theorem are known and apply more generally to certain quadratic algebras in the Koszul setting. The term "PBW deformation" is now standard. This talk will be a survey of the PBW theorems, contemporary uses of the theorems, and their relation to deformation theory. Examples of quadratic algebras in which the PBW theorem does not apply will also be given.