  We analyze an interacting Bose-Fermi mixture in a 1D disordered potential
using a combination of renormalization group and variational methods. We obtain
the complete phase diagram in the incommensurate case as a function of bosonic
and inter-species interaction strengths, in the weak disorder limit. We find
that the system is characterized by several phase transitions between
superfluid and various glassy insulating states, including a new Bose-Fermi
glass phase, where both species are coupled and localized. We show that the
dynamical structure factor, as measured through Bragg scattering experiments,
can distinguish between the various localized phases and probe their dynamics.
