The physical principles of dual-energy computed tomography (DECT) are as old as computed tomography (CT) itself. To understand the strengths and the limits of this technology, a brief overview of theoretical basis of DECT will be provided. Specific attention will be focused on the interaction of X-rays with matter, on the principles of attenuation of X-rays in CT toward the intrinsic limits of conventional CT, on the material decomposition algorithms (two- and three-basis-material decomposition algorithms) and on effective Rho-Z methods. The progresses in material decomposition algorithms, in computational power of computers and in CT hardware, lead to the development of different technological solutions for DECT in clinical practice. The clinical applications of DECT are briefly reviewed in relation to the specific algorithms.