Searches for long-lived particles at accelerators

The scientific community's interest in discovering long-lived new physics particles has intensified in recent years. These particles, elusive due to their tiny interactions, represent a significant area of inquiry in particle physics. This talk will focus on recent progress in this field, highlighted by two case studies: the Downstream algorithm at LHCb and the SHiP experiment, representing searches at the LHC and utilizing extracted beamlines. The discussion will cover the capacity of these experiments to exclude a range of particle signatures, a vital step in the search process. Furthermore, in the event of a positive detection, the talk will address the methodologies employed by these experiments to determine the properties of these long-lived particles. Such discoveries could provide essential insights into phenomena that extend beyond the standard model of particle physics.