Decays of B mesons into purely leptonic final states offer a wide range of observables to test the Standard Model (SM) of particle physics and to observe indirect hints of New Physics. For instance new features such as unexpectedly high Branching Fractions or violation of Lepton Flavour Universality can show up in such processes proving unambiguously the presence of new degrees of freedom at a scale larger than the electroweak one. The theory predictions for such observables (such as the aforementioned Branching Fractions or the effective lifetime) are very precise and the experimental searches for some of these channels (e.g. B_s -> μ+ μ-) are now entering a precision measurement regime. I will review the motivation and the main observables related to these processes and I will present the current status of the experimental searches (lead by LHCb and Belle) along with the prospects for the future (from LHCb and Belle 2).