variational integrators preserve geometric and topological structure when applied to hamiltonian systems. most of the research into variational integrators has focused upon their derivation by discretizing hamilton's principle as a type i generating function of the symplectic map. in this talk we examine the derivation of variational integrators from a type ii generating function. even when the maps resulting from different generating functions are analytically equivalent there can be important numerical differences. we introduce a new class of variational integrators based on the taylor method and an augmented shooting method. the role of automatic differentiation for an efficient implementation is discussed. finally, a new framework for adaptive variational integrators is presented, which is dependent upon hamiltonian variational integrators.