Aging degradation and seismic damage of civil infrastructures have become a serious issue for society, and one promising technology for monitoring their conditions is optical fiber sensing. Glass optical fibers have been predominantly used for the past several decades to develop fiber sensors, but currently polymer or plastic optical fibers (POFs) have also been used extensively to develop advanced fiber sensors because of their unique features, such as high flexibility, large breakage strain, and impact resistance. This review focuses on recently developed distributed and quasi-distributed POF-based sensing techniques based on Rayleigh scattering, Brillouin scattering, and fiber Bragg gratings.