The development of the kinetic-energy density functional (KEDF) is known as the most difficult task in the density-functional theory (DFT). Given that the history of the study of the KEDF began with the Thomas-Fermi (TF) model in 1927 (Thomas, Proc Camb Phil Soc 23:541, 1927, [1]), almost a century has been devoted to the functional development. The aim of this chapter is to present an overview of the history of the KEDF and also to provide the details of the recent developments utilizing the energy electron density \(n^e\) based on the novel DFT framework introduced in Chap.  3 . The TF model and the Weizäcker correction is reviewed in Sect. 5.1, where an approach by Wang and Teter (Phys Rev B 45(23):13196, 1992, [2]) to incorporate a nonlocal kernel into the KEDF is also introduced. In Sect. 5.2, the WT nonlocal functional is reconsidered in the formalism of the Taylor expansion of the KEDF up to the 2nd-functional derivative to generalize their approach. Then, in Sect. 5.3, a nonlocal KEDF is developed for the distribution \(n^e(\epsilon )\) on the energy coordinate \(\epsilon \) . The important feature of the method is that the nonlocal kernel employs the response function for the molecule of interest and not for the homogeneous electron gas, in contrast to the WT functional. The fatal problem with the TF model is that it does not provide a sound potential energy profile of a dissociating chemical bond. In Sect. 5.4, the mechanism underlying the failure is elucidated, and a functional that resolves the problem is developed in parallel to the static correlation functional in Chap.  4 . In this chapter, the atomic units (a.u.) are used unless otherwise stated.