  We consider isolated quantum systems with all of their many-body eigenstates
localized. We define a sense in which such systems are integrable, and discuss
a method for finding their localized conserved quantum numbers ("constants of
motion"). These localized operators are interacting pseudospins and are subject
to dephasing but not to dissipation, so any quantum states of these pseudospins
can in principle be recovered via (spin) echo procedures. We also discuss the
spreading of entanglement in many-body localized systems, which is another
aspect of the dephasing due to interactions between these localized conserved
operators.
