It is possible to devise quantum information protocols whose correctness can be certified even when they are run with untrusted quantum devices, on which no a priori assumptions are made. Hence the name 'device-independence' (DI) to refer to such protocols. It allows for certifiable cryptographic randomness generation (RNG) and key distribution (QKD) with unprecedented security. A promising path to the design of more experimentally friendly protocols is to make stronger assumptions on the devices, keeping the spirit of device independence while acknowledging differences in the level of trust about the quantum devices used that can be justified in the context of a realistic implementations. Practical implementations also reveal the limits of the device-independent model: as any model for security, device-independence makes a set of assumptions, such as perfect isolation of the trusted users' laboratories, that may in practice be compromised. Beyond key distribution, it is interesting to investigate if the device-independent approach to security can be extended to other tasks in multi-party cryptography.