In this talk, after recalling some general results on elliptic curves and isogenies, I will present, the various key exchange techniques based on isogenies between, namely Couveignes-Rostovtsev-Stolbunov, SIKE and CSIDH.
Then, I give a description of the main ideas that led Decru and Castryck to a devastating attack on SIKE. This talk is *not* the presentation of personal results.