Studying phase structure in localized systems requires us to first formulate a sharp notion of a phase away from thermal equilibrium. This is done via the notion of eigenstate order : one can measure order parameters and correlation functions in individual energy eigenstates of a many-body system, instead of averaging over several eigenstates as in a Gibbs state. The key point is that individual eigenstates can show patterns of order that may be invisible to thermodynamic averages over eigenstates. Indeed, a thermodynamic ensemble average isn't even appropriate in MBL systems since they never reach thermal equilibrium. What's more, while individual eigenstates aren't themselves experimentally accessible, order in eigenstates nevertheless has measurable dynamical signatures. The eigenspectrum properties change in a singular fashion as the system transitions between from one type of MBL phase to another, or from an MBL phase to a thermal one---again with measurable dynamical signatures.