<p>Recent advances in superconducting materials are giving renewed impetus to different power applications, some of which already existed based on previous superconductors with more modest properties while some others have been the symbiosis of new requirements in science and technology and better properties of the new superconductors. This paper constitutes a review of classical and new superconducting materials for power applications (the technological superconductors as they are frequently called) in terms of their structure and their engineering properties (electrical, mechanical and thermal) but also in terms of their manufacturability and scalability for possible scenarios where massive quantities may be required. The second and longer part of the paper is a state of the art of power applications of superconductivity related to energy (generation, transport and transmission), transport (airborne, waterborne and terrestrial) and industrial processes. Practically, all these applications are based on superconducting magnets, which are addressed in the article, including new technologies regarding their design, fabrication and operation. Particularly, these magnets can be the coils of superconducting electrical machines, also described in the paper, where different applications are presented following a scheme of problems to be solved versus the solution provided by superconductivity, including benefits regarding sustainability improvement associated with their better efficiency and power consumption reduction.</p>