The experimental demonstration of current-driven spin-transfer torque (STT) for switching magnets and push domain walls (DWs) in magnetic nanowires have opened up new avenues for spintronic computations. These devices have shown great promise for logic and memory applications due to superior energy efficiency and nonvolatility. It has been noted that the nonlinear dynamics of DWs in the physical magnetic system is an untapped source of entropy that can be leveraged for hardware security. The inherent noise, spatial, and temporal randomness in the magnetic system can be employed in conjunction with microscopic and macroscopic properties to realize novel hardware security primitives. Due to simplicity of integration, the spintronic circuits can be an add-on to the silicon substrate to complement the existing CMOS-based security and trust infrastructures. This paper investigates the prospects of spintronics in hardware security by exploring the security-specific properties and novel security primitives realized using spintronic building blocks. As spintronic elements enter the mainstream computing platforms, they are exposed to emerging attacks that were infeasible before. This paper covers the security vulnerabilities, security and privacy attack models, and possible countermeasures to enable safe computing environment using spintronics.