We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unit filling, which has been controversial for many years.  We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder: the Bose-glass phase always intervenes between the Mott insulating and superfluid phases.
This conclusion follows from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line.  A highly nontrivial overall shape of the phase diagram is revealed with the worm algorithm.  The phase diagram features a long superfluid finger at strong disorder and on-site interaction.  Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth.