The demand for Internet of Things services is increasing exponentially, and consequently a large number of devices are being deployed. To efficiently authenticate these objects, the use of physical unclonable functions (PUFs) has been introduced as a promising solution for the resource-constrained nature of these devices. The use of machine learning PUF models has been recently proposed to authenticate the IoT objects while reducing the storage space requirement for each device. Nonetheless, the use of a mathematically clonable PUFs requires careful design of the enrollment process. Furthermore, the secrecy of the machine learning models used for PUFs and the scenario of leakage of sensitive information to an adversary due to an insider threat within the organization have not been discussed. In this paper, we review the state-of-the-art model-based PUF enrollment protocols. We identity two architectures of enrollment protocols based on the participating entities and the building blocks that are relevant to the security of the authentication procedure. In addition, we discuss their respective weaknesses with respect to insider and outsider threats. Our work serves as a comprehensive overview of the ML PUF-based methods and provides design guidelines for future enrollment protocol designers.