Beyond the Standard Model physics in the far-forward region of the Large Hadron Collider

A new physics program has been initiated as part of the ongoing LHC physics run in the far-forward region, where dedicated FASER and SND@LHC experiments are currently taking data. We discuss the possible discovery prospects of this program in the search for signatures of beyond the Standard Model physics. We focus on both the present period and the proposed future Forward Physics Facility (FPF) that will operate in the high luminosity LHC era.