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Quantum systems bring unprecedented advantages to the realization of classical cryptographic tasks. A remarkable example is quantum key distribution, which allows two parties, Alice and Bob, to establish a secret key that can be used for unconditionally secure communication. Furthermore, the strong correlations exhibited by quantum systems can be explored to construct cryptographic protocols that are secure even when the parties are completely ignorant about the internal working of their devices. This is the device-independent paradigm. In this talk I will introduce the device-independent scenario and review recent results on device-independent quantum key distribution. Then I will move to the case of many parties and discuss extensions to multipartite cryptographic tasks. Finally, I will present new results where we introduce the paradigm of self-testing with dishonest parties and design a protocol for device-independent certification of the quantum state distributed in a network when some of the nodes may collude and act dishonestly.