The interest in the mechanical behavior of shape memory alloys (SMAs) is rapidly growing with the increasing number of potential industrial applications. In most applications, SMAs experience general non-proportional thermo-mechanical loadings. Thus, according to experimental observations, the so-called variant reorientation should be considered in the constitutive model development. In this monograph, the SMA behavior under multiaxial loadings at small and finite deformations is investigated. It is shown that most available SMA models are basically the same under proportional loadings while they yield different results under non-proportional loading conditions. Based on the multiplicative decomposition of the deformation gradient into elastic and inelastic, several finite deformation SMA constitutive models are proposed. A model which utilizes interesting properties of the logarithmic strain is also introduced. A part of this monograph is devoted to numerical implementation of the proposed constitutive models. Several SMA-based applications, i.e., an SMA spring, a Nitinol stent and a smart micro-gripper are simulated.