Reconstruction techniques and physics case for displaced tracks and vertices at LHC

The primary focus of the LHC experiments was the observation of Standard Model particles and the search for unexplored signatures indicative of New Physics. Given the current discoveries and measurements done so far, the detectors and the trigger architecture are being changed to allow for the searches of long-lived particles. LHCb's trackers have excelled in the precise reconstruction of heavy flavour hadrons, and the experiment is now at the forefront of designing flexible trigger systems. Similarly, ATLAS and CMS, with their precise trackers, are also exploring new avenues by implementing innovative triggers to search for long-lived particles. The techniques of the reconstruction of displaced tracks and vertices in the upgraded LHCb detector, complementary with other general-purpose detectors at the LHC, are presented in this proceedings.