In 1976, two cryptographers Diffie and Hellman have proposed a way to share a secret key between two people, say Alice and Bob. For this construction, Alice and Bob first need to agree on a group to build on their shared secret. Several generalizations of this protocol have been proposed in the years. In this talk we will discuss how such protocols can be constructed from elliptic curves, widely used in elliptic curve cryptography. Namely, we will focus on two key exchange protocols: first, the classical ECDH (Elliptic Curve Diffie-Hellman) and the more recent, conjecturally quantum-secure, SIDH (Supersingular Isogeny Diffie-Hellman) by De Feo, Jao and Plût, from 2011. We will first start by a suitable framework to study such key-exchange protocols by recalling the Diffie-Hellman protocol. In a second step, we will give the necessary mathematical background on elliptic curves to explain the construction of SIDH. Herefore, we mainly work with isogenies between elliptic curves, that are special group morphisms. We will also focus on some algorithmic questions related to the problem.