This survey reviews various methods for modeling the electrical resistance of Shape Memory Alloy (SMA) wires, emphasizing the classical approach and its relationship with advanced methodologies. SMAs belong to a unique class of materials exhibiting phase-dependent electrical resistance behavior, driven by temperature-induced phase transformations between austenite and martensite. The classical approach correlates resistance with fundamental parameters such as temperature, stress, strain, and martensitic volume fraction. In contrast, higher-order models, including empirical, thermodynamic, micromechanical, and phase transformation kinetics-based approaches—provide deeper insights by incorporating phenomena such as hysteresis, transformation strain, and phase heterogeneity. This paper evaluates these modeling techniques in terms of accuracy, computational complexity, and applicability to SMA-based systems such as actuators, sensors, and biomedical devices. A comparative analysis highlights the trade-offs between model precision and computational efficiency, offering a comprehensive evaluation of their suitability for different applications.