Neutrinoless double-beta decay is a very rare, yet unobserved, weak decay mode, where in a nucleus two neutrons decay into two protons, only emitting two electrons. The absence of (anti)neutrinos has deep consequences: lepton number conservation is violated, and neutrinos would be their own antiparticles (Majorana particles). In addition, if the nuclear matrix elements of the decay are known, the experimental lifetime of the process can be used to extract the absolute masses of the neutrinos, and the neutrino mass hierarchy. I will give an overview of neutrinoless double-beta decay and its consequences, and discuss some of the theoretical challenges faced in the calculation of the nuclear matrix elements of this process. This includes using many-body techniques for the nuclear structure description of the initial and final nuclei of the decay (calcium, germanium, selenium, tellurium or xenon), and also the derivation of the transition operator taking into account the interactions between nucleons in the decaying process.