  We present an asymptotically exact renormalization-group theory of the
superfluid--insulator transition in one-dimensional disordered systems, with
emphasis on an accurate description of the interplay between the
Giamarchi--Schulz (instanton--anti-instanton) and weak-link (scratched-XY)
criticalities. Combining the theory with extensive quantum Monte Carlo
simulations allows us to shed new light on the ground-state phase diagram of
the one-dimensional disordered Bose-Hubbard model at unit filling.
