This paper gives the survey of the advances in the theory and practice of the p and h-p versions of the finite element method. It gives the extensive list of references related to recent results of this new approach. The finite element method has become the main tool in computational mechanics. The MAKABASE contains at present the information on approximately 1400 finite/ boundary element programs, about 20,000 references on finite element and 2,000 boundary element technology. To date there are more than two hundred monographs and proceedings. Recently a new direction in the finite element theory and practice appeared, the p and h-p versions which utilizes high degree elements. About 3-4 dozens references (out of 22,000) and only few programs are available. The aim of the paper is to briefly survey the state of the art about the p and h-p versions and present the basic references. We restrict ourself to the most simple but a characteristic model problem for elliptic partial differential equations.