MoEDAL is a pioneering experiment designed to search for highly ionising messengers of new physics such as magnetic monopoles or massive (pseudo-)stable charged particles, that are predicted to exist in a plethora of models beyond the Standard Model. Its ground-breaking physics program defines a number of scenarios that yield potentially revolutionary insights into such foundational questions as, are there extra dimensions or new symmetries, what is the mechanism for the generation of mass, does magnetic charge exist, what is the nature of dark matter, and, how did the big-bang develop at the earliest times. MoEDAL's purpose is to meet such far-reaching challenges at the frontier of the field. The physics reach of the existing MoEDAL detector is discussed, giving emphasis on searches for magnetic monopoles, supersymmetric (semi)stable partners, doubly charged Higgs bosons, and exotic structures such as black-hole remnants in models with large extra spatial dimensions and D-matter in some brane theories.