In this talk we discuss Ore Extensions, a type of non-commutative algebra which includes Weyl algebras and quantum polynomial rings as special cases. We will give motivating examples and consider iterated generalizations like certain universal enveloping algebras. Resolutions provide important tools for studying non-commutative algebras, but practical resolutions, like the Chevalley-Eilenberg complex, have been elusive for many classes of algebras including Iterated Ore Extensions. We will present the notion of a twisted tensor product and explain how these are used to construct new resolutions for Iterated Ore Extensions.