A quantum computer would break the currently deployed public key cryptosystems. In light of this, NIST is currently organizing a public evaluation of "quantum-secure'' cryptographic protocols. Protocols whose security is based on the hardness of computing isogenies between supersingular elliptic curves have been suggested for hashes, public key encryption, and signature schemes. Breaking these systems involves either computing an isogeny of prime-power degree between two given supersingular elliptic curves, or computing the endomorphism ring of a given curve. In this talk, I will discuss how cryptosystems are built using supersingular isogenies, and how the problem of computing isogenies reduces to the problem of computing endomorphism rings.