The increase of energy demand added to the concern for environmental pollution linked to energy generation based on the combustion of fossil fuels has motivated the study and development of new sustainable ways for energy harvesting. Among the different alternatives, the opportunity to generate energy by exploiting the osmotic pressure difference between water sources of different salinities has attracted considerable attention. It is well-known that this objective can be accomplished by employing ion-selective dense membranes. However, so far, the current state of this technology has shown limited performance which hinders its real application. In this context, advanced nanostructured membranes (nanoporous membranes) with high ion flux and selectivity enabling the enhancement of the output power are perceived as a promising strategy to overcome the existing barriers in this technology. While the utilization of nanoporous membranes for osmotic power generation is a relatively new field and therefore, its application for large-scale production is still uncertain, there have been major developments at the laboratory scale in recent years that demonstrate its huge potential. In this review, we introduce a comprehensive analysis of the main fundamental concepts behind osmotic energy generation and how the utilization of nanoporous membranes with tailored ion transport can be a key to the development of high-efficiency blue energy harvesting systems. Also, the document discusses experimental issues related to the different ways to fabricate this new generation of membranes and the different experimental set-ups for the energy-conversion measurements. We highlight the importance of optimizing the experimental variables through the detailed analysis of the influence on the energy capability of geometrical features related to the nanoporous membranes, surface charge density, concentration gradient, temperature, building block integration, and others. Finally, we summarize some representative studies in up-scaled membranes and discuss the main challenges and perspectives of this emerging field.