In 1984, C.H. Bennet and G. Brassard proposed a new protocol aimed to solve the problem of symmetric cryptographic key exchange. This protocol was called BB84 after the name of its authors. While a traditional method would rely on public key cryptography (like RSA), the BB84 protocol takes benefit of the laws of quantum mechanics, like for example the fact that any quantum measurement can perturb the system. Traditional public key algorithms security often rely on a typical hard mathematical problem. It is well known for example that the ability to factorize easily any number would make the usage of RSA completely insecure. Quantum Key Exchange (QKE) protocols security cannot be proved in a similar way. In this work, we will try to give an overview of security proofs of quantum key exchange protocols, focusing on the BB84 protocol.