In some variations, the invention provides a curable adhesive formulation comprising a curable liquid precursor capable of frontal polymerization, wherein the liquid precursor comprises a monomer and a polymerization catalyst, and frontal-polymerization-triggering susceptors in contact with, or contained within, the liquid precursor. The susceptors may include conducting and/or magnetic solid particles capable of induction heating in the presence of a remotely applied electromagnetic field. Other variations provide a polymer-curing system comprising a curable liquid precursor, frontal-polymerization-triggering susceptors, and an apparatus configured to remotely produce an alternating electromagnetic field in line-of-sight with the susceptors (but not necessarily in line-of-sight with the liquid precursor), thereby generating induction heating to initiate the frontal polymerization. The susceptors may be about 0.1 wt % to about 50 wt % of the curable formulation. Other variations provide a method of curing an adhesive joint through an opaque barrier.