The incorporation of heteroatom-containing weak bonds along polymer backbones has become a popular tool to accelerate degradation. Many methods have already been reported for the synthesis of degradable heteroatom-containing polymers based mainly on conventional step-growth polymerization and chain-growth ring-opening polymerization (ROP). In recent years, ring-opening metathesis polymerization (ROMP) has evolved as an emerging approach for the synthesis of various types of degradable polymers, from carbocyclic norbornene derivatives to heterocyclic olefin monomers. Classic ruthenium (Ru)-based catalysts exhibit not only high reactivity to C=C double bonds but also high tolerance to polar functional groups. Hence, a rich range of functional groups can be incorporated into cyclic olefin monomers and then transferred to the polymer backbones. This review covers the synthesis of the various heteroatom-containing degradable (co)polymers via ROMP, including poly(thio)acetals/polyketals, polyorthoesters, polyesters, polycarbonates, polyphosphoesters/polyphosphoamidates, poly(enol ether)s, poly(silyl ether)s, polydisulfides, polyketones, polyacylsilanes, polyamides, and polyureas, as well as their degradable mechanisms under different conditions. The review also highlights applications in tissue engineering and medicine.