Quantum key distribution is well known to be an essentially quantum task, which is not possible by purely classical means. After being suggested on the basis of strongly nonclassical single-photon states and direct photodetection in the discrete-variable approach, it was later extended to continuous variables, using Gaussian states and coherent detection, well known in classical optical communication. We will therefore discuss the role of nonclassicality and non-Gaussianity in quantum key distribution with discrete and continuous variables, reveal the role of nonclassical resources in security and robustness of the protocols, and consider their extension to multiple users.