The observation of Bell nonlocality without signaling is a signature of quantum entanglement. Starting in 2007, this observation was made quantitative: nonlocality can be used to estimate the amount of entanglement, the number of extractable random bits, the length of a secret key... This type of estimates has been called "device-independent" (DI), since it relies only on the validity of quantum theory and on observation, without the need for any knowledge of the degrees of freedom under study. 

In some cases, DI certification can go as far as identifying uniquely the quantum state that is used and the measurements that are performed. This observation, which has been called "DI self-testing", had been anticipated in nonlocality [Werner and Summers (1987), Popescu and Rohrlich (1992)] and in the context of quantum cryptography [Mayers and Yao (1998)]. Starting from this double birth, I shall review the notion of self-testing and a number of results that have been obtained in the last few years.