Over the last 20 years, thin and lightweight optical elements have become very desirable, especially for the terahertz (THz) range. Reduction of the volume of optical elements alongside an increase in their effective efficiency has begun a new direction of research leading to many practical applications. On top of that, diffractive optical elements can not only focus the incident beam, but also can shape the incoming wavefront into a desirable distribution or can redirect the energy. Starting from theoretical calculations of Fourier optics, diffractive elements have been transformed and nowadays form complicated structures that do not resemble a typical Fresnel lens. The precise control over a phase shift introduced by the designed element creates an opportunity to almost freely transform an incident wavefront. Moreover, the vast diversity of computer-generated holograms (also called synthetic) contributes substantially to this topic. Diffractive elements have a great impact on THz optical systems because their manufacturing is very simple in comparison with any other range of radiation (infrared, visible, ultraviolet, etc.). This review paper underlines developments in evolution of diffractive optics and highlights main principles and technological approaches for fabrication of diffraction optics within the terahertz range, thus serving as a guide to design and production considerations.