This chapter explores the design and architecture of advanced Physically Unclonable Functions (PUFs) to meet changing security needs. It introduces memory-based implementations like the Mem-APUF, as well as temporal shadow PUFs that use new techniques for improved security and reliability. It also examines the balance between randomness, uniqueness, and security in these designs and how they can be adjusted to suit different applications. By considering both hardware and algorithmic innovations, this chapter offers insights into the development of advanced PUF architectures to enhance security in IoT, cryptographic systems, and other secure applications.