The Yangian is an infinite-dimensional quantum group deforming the universal enveloping algebra of the algebra of Lie algebra-valued polynomials in one variable. Double Yangians are quantum groups deforming the universal enveloping algebra of Lie algebra valued polynomials in two variables. I will discuss the construction of double Yangians for type A, some of the structures present on these algebras, and a quantum field theory related to these algebras. If time permits, I will also mention a relationship to categorified Donaldson-Thomas invariants.