A systematic framework for the synthesis and/or retrofit of flexible and structurally controllable heat exchanger networks is presented in this paper. Based on a multiperiod hyperstructure network representation, explicit structural controllability (total disturbance rejection) criteria are developed and included within a synthesis/retrofit mixed-integer nonlinear programming model, where a total annualized (operating and investment) cost is minimized. The proposed framework results in a network structure which features minimum annualized cost, while being (i) flexible to operate within a specified range (or discrete set) of uncertain stream flow rates, inlet temperatures, and/or heat transfer coefficients and (ii) structurally controllable for a given set of disturbances and control variables.