In this talk, we study how to use gradient/derivative recovery techniques to formulate error estimate and error indicator for p-adaptive FEMs, where elements are allowed to have variable degrees. The study also suggests an approach to implement a fully automatic hp-adaptive FEM. In this approach, the decision on whether to refine a given element into two child elements (h-refinement) or increase its degree (p-refinement) is made heuristically purely on information from error estimate. Several numerical results will be presented to show the efficiency of the methods.