The detection of the Higgs boson in 2012 raised hopes for rapid discovery of Physics Beyond the Standard Model at the LHC, however, the search for New Physics turned out to be much more difficult than anticipated. The lack of a positive result led to a growing interest in previously unexplored exotic signatures, e.g. long-lived particles. In the talk, I will discuss different search strategies for long-lived particles at the LHC. Special emphasis will be put on the prospects for the detection of long-lived particles in the MoEDAL experiment, which had been primarily designed to search for magnetic monopoles, but can also be utilised to detect semi-stable charged particles. Prospects for the detection of long-lived particles at the end of Run 3 and HL-LHC phases will be presented, and a comparison between different search strategies in MoEDAL, ATLAS and CMS experiments will be made.