In this talk we will review recent advances in the implementation of specific types of Nedelec Curl-Conforming (or 1 form) and Divergence Conforming (or 2-form) basis functions and their corresponding degrees of freedom. These basis functions are derived from the H(Curl) and H(Div) conforming polynomial spaces originally proposed by Nedelec and can be used in a variety of finite element computations. We present both interpolatory and hierarchical bases. For the interpolatory case, we demonstrate a basis which yields optimal growth of finite element matrix condition number as a function of the polynomial degree of the basis. For the hierarchical case, we present basis functions and degrees of freedom which can be used in a p-refinement setting by providing a means for joining together elements of different local approximation orders. For each case, a method for ensuring the global connectivity of elements in an unstructured 3D mesh environment is presented. We also present preliminary results for special mass lumping techniques using the new family of finite elements proposed by Nedelec in 1986.