In this review, a comparative analysis of the literature and our own results obtained in the study of the physicochemical, dielectric, and proton-conducting properties of composite polymer materials based on 1H-1,2,4-triazole has been carried out. It has been established that 1H-1,2,4-triazole and homopolymers and copolymers of 1-vinyl-1,2,4-triazole are promising for the development of proton-conducting fuel cell membranes. They significantly improve the basic characteristics of electrolyte membranes, increase their film-forming ability, increase thermal stability up to 300–330 °C, increase the electrochemical stability region up to 3–4 V, promote high mechanical strength and morphological stability of membranes, and provide high ionic conductivity (up to 10−3–10−1 S/cm) under anhydrous conditions at temperatures above 100 °C. There is also an improvement in the solubility and a decrease in the glass transition temperature of polymers based on 1-vinyl-1,2,4-triazole, which facilitates the processing and formation of membrane films. The results obtained demonstrate the uniqueness of 1H-1,2,4-triazole and (co)polymers based on 1-vinyl-1,2,4-triazole and the promise of their use for the creation of heat-resistant plastic and electrochemically stable, mechanically strong proton-conducting membranes with high ionic conductivity under anhydrous conditions and at high temperatures.