Brief history of terahertz (THz) and infrared (IR) science and technology, for learning lessons by historical evolution is presented and discussed identifying important (from Author's point of view) steps for their development. THz still is the not well-known region of electromagnetic science, even it has been lightened by starting of scientific and technological knowledge, since the end of 19 th century. As concerning history of IR science and technology, it took many years since 1800 (W. Hershel) to reach the level of use that is recognized today. The link between IR and thermal science and applications was so strong that IR was for a long time synonymous of thermography. THz science and technology are showing a rapid growth. IR and, especially THz technologies, now have become one of the major fields of applied research. Nowadays, they become widely spread in their use in astrophysics, security, biomedicine, detection of hidden objects, food and art inspection, etc. The increasing requirements for fast transmission of large amounts of data will lead to the extension of operation frequencies in communications toward the THz frequency range. IR and THz medical imaging can provide guidance for surgeons in delimiting the tumor margins, help clinicians visualize diseased area, etc. A few decades ago, IR technologies were mainly the domain of military ones. In recent two decades, due to widespread of lowcost thermal uncooled arrays there were realized many IR technology advances in civil and military applications. A large amount of THz technologies mass-market applications can't be highlighted, as these technologies do not meet yet the user requirements, especially in easiness of use and costs. Still, many of THz applications that we have now are emerging and showing their applicability in some implementations, where other methods can't give any comprehensive information, e.g., in dry food inspection for dielectric inclusions, skin tumour margins control, THz astronomy, package and envelope inspection, etc. The brief lessons given by historical highlights in THz and IR science and applications can be important for the future developments in these directions as history frequently opens routes for new thinking. In this brief review, the missed important steps can happen. Author apologizes for these possible faults.