Shape Memory Alloys (SMAs) are unique materials with a paramount potential for various applications in bridges. The novelty of this material lies in its ability to undergo large deformations and return to its undeformed shape through stress removal (superelasticity) or heating (shape memory effect). In particular, Ni-Ti alloys have distinct thermomechanical properties including superelasticity, shape memory effect, and hysteretic damping. SMA along with sensing devices can be effectively used to construct smart Reinforced Concrete (RC) bridges that can detect and repair damage, and adapt to changes in the loading conditions. SMA can also be used to retrofit existing deficient bridges. This includes the use of external post-tensioning, dampers, isolators and/or restrainers. This paper critically examines the fundamental characteristics of SMA and available sensing devices emphasizing the factors that control their properties. Existing SMA models are discussed and the application of one of the models to analyze a bridge pier is presented. SMA applications in the construction of smart bridge structures are discussed. Future trends and methods to achieve smart bridges are also proposed.