  We study the superconductor-insulator quantum phase transition in disordered
Josephson junction chains. To this end, we derive the field theory from the
lattice model that describes a chain of superconducting islands with a
capacitive coupling to the ground ($C_0$) as well as between the islands
($C_1$). We analyze the theory in the short-range ($C_1 \ll C_0$) and in the
long-range ($C_1 \gg C_0$) limits. The transition to the insulating state is
driven by the proliferation of quantum phase slips. The most important source
of disorder originates from trapped charges in the substrate that suppress the
coherence of phase slips, thus favoring superconducting correlations. Using the
renormalization-group approach, we determine the phase diagram and evaluate the
temperature dependence of the dc conductivity and system-size dependence of the
resistance around the superconductor-insulator transition. These dependences
have in general strongly non-monotonic character, with several distinct regimes
reflecting an intricate interplay of superconductivity and disorder.
