Shape memory alloys (SMA) undergo reversible martensitic transformation in response to changes in temperature or applied stress, resulting in the properties of superelasticity and shape memory. At present, there is high scientific and technological interest to develop these properties at small scales and apply SMA as sensors and actuators in microelectromechanical system technologies. To study the thermomechanical properties of SMA at micro and nanoscales, instrumented nanoindentation is widely used to conduct nanopillar compression tests. By using this technique, superelasticity and shape memory at the nanoscale have been demonstrated in micro and nanopillars of Cu-Al-Ni SMA. However, the martensitic transformation seems to exhibit different behavior at small scales, and a size effect on superelasticity has been recently reported. In this study, we provide an overview of the thermomechanical properties of Cu-Al-Ni SMA at the nanoscale, with special emphasis on size effects. Finally, these size effects are discussed in light of the microscopic mechanisms controlling the martensitic transformation at the nanoscale.