Internet of Things connected many useful electronic devices to each other through the internet, and sharing private and sensitive data between these devices needs secure access and communication. One of the best solutions for this purpose is hardware security primitives such as Physically Unclonable Functions (PUFs). PUFs are cryptographic primitives that are employed to produce a unique and reliable digital fingerprint for a particular electronic circuit. This digital fingerprint is used in many security applications such as chip identification, authentication, and secret key storage and generation. The emergence of memristors (Memory-Resistor) as new nanotechnologies are utilized extensively in hardware security applications such as Memristive PUFs. Research progress in Memristive PUFs resulted in improved performance metrics of PUFs due to memristors' unique characteristics. This article provides an investigation of different design approaches of Memristive PUFs that were introduced in the literature. Then, provide detailed performance evaluation results obtained by simulation and fabrication processes for different Memristive PUFs designs, and make a comparison between these results. Finally, concluded that most of the circuits are evaluated by simulation, whereas few other circuits were evaluated by fabrication owing to the expensive fabrication process. Since the memristor is a prototype and not commercialized yet, it is expected to be adopted and marketed in the next generation of hardware security.