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This article provides a comprehensive review of experimental work on security primitives based on emerging and mature nonvolatile memories (NVMs). The focus is on physically unclonable functions (PUFs) that exploit process-induced variations to generate a die-specific random response. We identify two main types of the proposed designs and discuss their advantages and main challenges. Endurance and reliability are serious concerns in PUFs relying on large-signal stochastic switching properties of NVMs in the verification phase. Such designs do not seem to be appealing in terms of energy, throughput, and security. On the other hand, circuit primitives that exploit sneak-path current and device nonlinearity are genuinely more suitable for building strong PUFs, but they are susceptible to environmental variations. Achieving high reliability in such PUFs is the main challenge, and finding a practical holistic solution with integrated optimum security and performance characteristics is an important research direction. We further note that many PUF works have been performed on a single memory cell level. The proposed implementations and their performance projected based on experimental data show a low bit error rate, however, at the cost of poor resilience to modeling attacks. Without further justification, these approaches can be only classified for now as weak PUFs, and moreover, more work would be needed to verify their physical unclonability. This article is concluded by outlining the most urgent experimental and modeling future work and the exciting prospects for NVM-based PUFs. [ABSTRACT FROM AUTHOR]