A fundamental understanding of structure-morphology-property relationships of proton exchange membranes (PEMs) is crucial in order to improve the cost, performance, and durability of PEM fuel cells (PEMFCs). In this context, there has been an explosion over the past five years in the volume of research carried out in the area of non-perfluorinated, proton-conducting polymer membranes, with a particular emphasis on exploiting phase behavior associated with block and graft copolymers. This progress report highlights a selection of interesting studies in the area that have appeared since 2005, which illustrate the effects of factors such as acid and water contents and morphology upon proton conduction. It concludes with an outlook on future directions.