Chemically modified graphene sheets can be readily prepared by chemical reduction of graphene oxide. Understanding the self-stacking behavior of chemically converted graphene (CCG) sheets is crucial to rational design of functional graphene-based bulk materials but has often been overlooked. This talk will highlight how our efforts to answer this question led to a number of surprising findings and the discovery of a new class of graphene hydrogel membranes. The applications of multilayered graphene hydrogel membranes in capacitive energy storage, smart membranes, nanofluidics and biomedicine will also be discussed.