One of the most rapidly developing areas of research in particle physics nowadays is to look for new, light, extremely weakly-interacting particles that could have avoided detection in previous years due to the lack of luminosity. These, so-called intensity frontier searches, have also broad cosmological connections to e.g. dark matter, as well as can help to unravel the mystery of neutrino masses. In this talk, we will summarize the current status of this field with a particular emphasis on a newly proposed experiment to search for such particles produced in the far-forward region of the LHC, namely FASER, the ForwArd Search ExpeRiment. FASER has been proposed as a relatively cheap detector to supplement traditional experimental programmes searching for heavy new physics particles in the high-pT region and, therefore, to increase the whole BSM physics potential of the LHC. On top of potentially far-reaching implications to BSM particle physics and cosmology, the newly proposed detector can also be used to measure high-energy SM neutrino cross sections providing the first neutrino measurement at the LHC.