A concise survey of superconducting power transmission (SPT) and associated topics is presented. After a brief background, which includes a summary of the probably now defunct low-temperature superconducting technology of the 1960s and 1970s, the article concentrates on the renaissance of interest in SPT with the advent of high-temperature superconductors (HTS) in the 1980s. AC and DC transmission and warm dielectric and cold dielectric conductors are discussed and some specific projects are outlined. State of the art is taken as current at the time of the Applied Superconductivity Conference 2004 [reported in IEEE Transactions in Applied Superconductivity 15 (2005)]. The benefits of HTS SPT are outlined, notably increased capacity and efficiency and its potential impact on energy conservation and the environment. The current state of development of HTS from first- to second-generation conductors is described, as is the possible role of magnesium diboride (MgB2). Examples of future trends evolving worldwide are given and, finally. an assessment of the capability and funding for applied superconductivity in the UK is made. (C) 2008 Queen's Printer and Controller of HMSO. Published by Elsevier Ltd. All rights reserved.