We address security and privacy problems for digital devices and biometrics from an information-theoretic optimality perspective, where a secret key is generated for authentication, identification, message encryption/decryption, or secure computations. A physical unclonable function (PUF) is a promising solution for local security in digital devices and this review gives the most relevant summary for information theorists, coding theorists, and signal processing community members who are interested in optimal PUF constructions. Low-complexity signal processing methods such as transform coding that are developed to make the information-theoretic analysis tractable are discussed. The optimal trade-offs between the secret-key, privacy-leakage, and storage rates for multiple PUF measurements are given. Proposed optimal code constructions that jointly design the vector quantizer and error-correction code parameters are listed. These constructions include modern and algebraic codes such as polar codes and convolutional codes, both of which can achieve small block-error probabilities at short block lengths, corresponding to a small number of PUF circuits. Open problems in the PUF literature from a signal processing, information theory, coding theory, and hardware complexity perspectives and their combinations are listed to stimulate further advancements in the research on local privacy and security.