The improved features of AC/DC converters, the need to enhance cross-country interconnections, the will to make massive remote renewable energy sources available, and the fear of populations about overhead lines have fostered HVDC cable transmission all over the world, leading in the last two decades to an exponential increase of commissioned HVDC cable projects, particularly of the extruded insulation type. Comprehensive surveys of the issues to be faced by HVDC extruded cable systems appeared in the literature some years ago, but they are not so up-to-date, as HVDC extruded cable technology is developing fast. Therefore, the contribution this paper aims at giving is a systematic, comprehensive and updated summary of the main present and future issues and challenges that HVDC cable systems have to face to further improve their performance and competitiveness, so as to meet the growing quest for clean and available energy worldwide. The topics covered in this review–treated in alphabetical order for the reader’s convenience–are accessories, higher voltage and power, laying environment (submarine and underground cables), modeling, multiterminal HVDC, operation and diagnostics, recyclable insulation, space charge behavior, testing, thermal stability, transient voltages.