Hardware security has emerged as an important field of study aimed at mitigating issues such as piracy, counterfeiting, and side channel attacks. One popular solution for such hardware security attacks are physical unclonable functions (PUF) which provide a hardware specific unique signature or identification. The uniqueness of a PUF depends on intrinsic process variations within individual integrated circuits. As process variations become more prevalent due to technology scaling into the nanometer regime, novel nanoelectronic technologies such as memristors become viable options for improved security in emerging integrated circuits. In this paper, we provide an overview of memristor based PUF structures and circuits that illustrate the potential for nanoelectronic hardware security solutions.