Real-time and continuous monitoring through smart sensors is considered to be the evolution of traditional track testing, enabling the earlier detection of the main failure modes that degrade railway tracks. Through carrying out preventive maintenance operations, infrastructure resources may be optimized, leading to smarter and more sustainable infrastructure. For this reason, under the larger goal of creating a synergy with various types of sensors for railway tracks, this article presents a critical review on the different, currently available sensors for smart and continuous monitoring. Specifically, the most appropriate monitoring technologies for each of the main railway track failure modes have been assessed and identified, thus deriving the advantages and capacities of each solution. Furthermore, this review presents some of the main experiences carried out to date in literature by using sensor technologies, such as strain gauges, piezoelectric sensors, fiber-optics, geophones and accelerometers. These technologies have proven to offer appropriate characteristics and accuracy for the continuous monitoring of a railway track’s structural state, being capable of measuring different parameters, such as deflections, deformations, stresses or accelerations that would permit the technical tracking of various forms of degradation.