In this talk I will introduce braided field theories, which are new classes of noncommutative field theories that are equivariant under a triangular Hopf algebra symmetry. They are constructed through a new mathematical notion of braided homotopy algebras. I will develop a braided generalization of the purely algebraic Batalin-Vilkovisky quantization techniques to explore the properties of braided quantum field theory. The techniques are illustrated by computing perturbative correlation functions for braided scalar field theories. The results of these calculations suggest that UV/IR mixing may be less severe or even absent in this class of noncommutative field theories.