Shape memory materials are smart materials that stand out because of several remarkable properties, including their shape memory effect. Shape memory alloys (SMAs) are largely used members of this family and have been innovatively employed in various fields, such as sensors, actuators, robotics, aerospace, civil engineering and medicine. Many conventional, unconventional, experimental and numerical methods have been used to study the properties of SMAs, their models and their different applications. These materials exhibit nonlinear behavior. This fact complicates the use of traditional methods, such as the finite element method and increases the computing time necessary to adequately model their different possible shapes and usages. Therefore, a promising solution is to develop new methodological approaches based on artificial intelligence (AI) that aims at efficient computation time and accurate results. AI has recently demonstrated some success inefficiently modeling SMA features with machine- and deep-learning methods. Notably, artificial neural networks (ANNs), a subsection of deep learning, have been applied to characterize SMAs. The present review highlights the importance of AI in SMA modeling and introduces the deep connection between ANNs and SMAs in the medical, robotic, engineering, and automation fields. After summarizing the general characteristics of ANNs and SMAs, we analyze various ANN types used for modeling the properties of SMAs according to their shapes, e.g., a wire as an actuator, a wire with a spring bias, wire systems, magnetic and porous materials, bars and rings, and re in forced concrete beams. The description focuses on the techniques used for NN architectures and learning.