  We construct a complete set of local integrals of motion that characterize
the many-body localized (MBL) phase. Our approach relies on the assumption that
local perturbations act locally on the eigenstates in the MBL phase, which is
supported by numerical simulations of the random-field XXZ spin chain. We
describe the structure of the eigenstates in the MBL phase and discuss the
implications of local conservation laws for its non-equilibrium quantum
dynamics. We argue that the many-body localization can be used to protect
coherence in the system by suppressing relaxation between eigenstates with
different local integrals of motion.
