The High Luminosity Large Hadron Collider (HL-LHC) is the new flagship project of CERN. First endorsed in 2013 and approved in 2016, HL-LHC is an upgrade of the accelerator aiming to increase by a factor of ten the statistics of the LHC collisions at the horizon of 2035–2040. HL-LHC relies on cutting edge technologies: among them, large aperture superconducting magnets will replace the present hardware to allow a smaller beam size in two interaction points (IPs). The project involves the construction of about 150 magnets of six different types: the quadrupole triplet, two main dipoles and three orbit correctors. The triplet, manufactured at CERN and in the USA, will consist of 30 magnets based on Nb₃Sn technology, with an operational peak field of 11.4 T. These will be the first quadrupole Nb₃Sn magnets installed in a particle accelerator. The other five types of magnets, all relying on Nb–Ti technology, present non-trivial challenges in the design and construction; they will be manufactured as part of in-kind contribution under the responsibility of institutes in Japan, China, Spain, and Italy. The project is now in the phase of transition between qualification through short models and prototypes and the beginning of the series construction. In this paper we review the magnet requirements, the reasons for selecting the design, the technological challenges with respect to previous projects, and we summarize the steps that have been taken to validate the baseline.