The Nédélec edge elements [1, 2] form the natural choices of basis functions to approximate electromagnetic fields, as the field tangential continuity is built into the basis functions. The edge elements have been applied extensively in microwave and optical devices [3]. In this chapter, we will first present the original construction of the Nédélec edge element basis including some mathematical detail. Then, explicit high-order hierarchical versions of the Nédélec basis with good conditioning properties will be presented.