Trapdoor claw-free functions (TCFs) are central to a recent wave of groundbreaking work in quantum cryptography that was originated by U. Mahadev and other authors.  TCFs enable protocols for cryptography that involve quantum computers and classical communication.  In this expository talk I will present the definition of a TCF and its variants, and I will discuss quantum applications, including the recent paper "Quantum Encryption with Certified Deletion, Revisited: Public Key, Attribute-Based, and Classical Communication" by T. Hiroka et al. (arXiv:2105.05393).