This book studies the security of Physical Unclonable Functions (PUFs) based on the Arbiter PUF design, with a focus on so-called modeling attacks. The author shows the insecurity of several designs and proposes a novel construction that is proven to be immune against attacks known in scientific literature. The book explores designs of variants and compositions of the Arbiter PUF, which was introduced as a CMOS-compatible, electrical PUF design, and has received a lot of research attention, albeit being insecure with respect to modeling attacks. After revisiting modeling attacks on the Arbiter PUF and XOR Arbiter PUF, the author demonstrates attacks against the Lightweight Secure XOR Arbiter PUF, Feed-Forward Arbiter PUF, and the Interpose PUF. He then introduces two novel PUF designs, the Beli PUF and the LP-PUF, and analyzes their security against modeling attacks. The book concludes by showing how the LP-PUF is resilient against currently known modeling attacks.