Osmotically driven membrane processes (ODMP) have gained renewed interest in recent years and they might become a potential solution for the world's most challenging problems of water and energy scarcity. Though the concept of utilizing osmotic pressure difference between high and low salinity streams across semipermeable membranes has been explored for several decades, lack of optimal membranes and draw solutions hindered competition between forward osmosis (FO) and pressure retarded osmosis (PRO) with existing water purification and power generation technologies, respectively. Driven by growing global water scarcity and by energy cost and negative environmental impacts, novel membranes and draw solutions are being developed for ODMPs, mass and heat transfer in osmotic process are becoming better understood, and new applications of ODMPs are emerging. Therefore, OMDPs might become promising green technologies to provide clean water and clean energy from abundantly available renewable resources. This review focuses primarily on new insights into osmotic membrane transport mechanisms and on novel membranes and draw solutions that are currently being developed. Furthermore, the effects of operating conditions on the overall performance of osmotic membranes will be highlighted and future perspectives will be presented.