Polyurethane is a highly versatile polymer that may be used in various types of applications with a wide range of properties. The combination of different types and ratios of isocyanate and polyol allows for the control of the desired end properties. Due to its unique properties, it has found applications in the fields of medical, military, automobile, and aerospace industries. Recently, there has been a prodigious interest in producing polyurethane-based smart polymers, especially shape memory polyurethane (SMPU). This is due to its excellent ability to change shape upon the application of external stimuli such as heat, electric field, magnetic field, and light. The existence of phase-separated structure known as soft- and hard-segment domains contributes toward the shape memory properties of polyurethane. The soft-segment domains are responsible for maintaining the temporary shape, while hard segments fix the permanent shape. This chapter comprehensively aims to address a wide overview of polyurethane-based smart polymer and the chemistry behind the shape memory properties. In addition, this chapter also summarizes the recent studies on the exploration of SMPU using vegetable oils along with petroleum-based polyol and the potential applications of smart polyurethane.