Since its discovery in the mid 20th century, most applications of alkyne metathesis have relied on thermodynamics to control product distributions. Ring-opening alkyne metathe- sis polymerization (ROAMP), in contrast, requires the kinetic product of metathesis of a strained, cyclic alkyne monomer to give a living, chain-growth polymerization (Chapter 1, Introduction). This living polymerization of conjugated alkyne-containing monomers has the potential to access a wide range of functional poly(arylene ethynylene) materials with excep- tional control over length, dispersity, topology, and endgroups. To this end, we demonstrate the first ROAMP synthesis of conjugated poly(ortho-phenylene ethynylene) and elucidate a mechanistic description of the reaction to understand the enabling catalyst selectivity and unexpectely find that initiator sterics dictate endgroup fidelity and polymer topology (Chap- ter 2). To disentangle the role of steric and electronic factors in initiator performance, we describe a novel synthetic method that gives a series of isosteric benzylidyne catalysts which exhibit a strong, deterministic electronic effect on both ROAMP initiation rates and polymer endgroup fidelity (Chapter 3). Finally, we develop an extension of this methodology to lever- age the alkynes from these living polymers to template the synthesis of telechelic graphene nanoribbons (GNRs) (Chapter 4). This work has not only uncovered mechanistic insights and design principles to improve ROAMP catalysts and facilitate access to hybrid poly- mer materials, but also demonstrated the potential of ROAMP to access other conjugated materials via post-polymerization modification of precision polymer templates.