Brain inspired electronics with organic memristors could offer a functionally promising and cost-effective platform for flexible, wearable, and personalized computing technologies. While there are different material approaches (viz. oxides, nitrides, 2D, organic) to realize memristors, organic materials are characteristically unique, as they could, in principle, offer spatially uniform switching, tunable molecular functionalities, and ultra-low switching energies approaching atto joules that are highly desirable but elusive with other material systems. However, despite a long-standing effort spanning almost 2 decades, the performance and mechanistic understanding in organic memristors are quite far from a translational stage and even a single suitable candidate is yet to emerge. Almost all the reported organic memristors lack reproducibility, endurance, stability, uniformity, scalability, and speed that are needed for an industrial application. In this review, we analyze the root cause of the prolonged failures of organic memory devices and discuss a new family of organic memristors, made of transition metal complexes of redox active organic ligands (RAL), that satisfy and go beyond the requirements specified in the 2015 ITRS roadmap for RRAM devices. These devices exhibit cyclability > 1012, retention of several months, on/off ratio > 103, switching voltage approaching 100 mV, rise time less than 30 ns, and switching energy <1 fJ, offering a quantum leap in organic memristor technology. This could give birth to a new generation of organic memristors that are industrially competitive with ample scopes for functional tunability by molecular engineering, such as variation of the metal center and ligands as well as the counterions. A combination of molecular and device engineering may enable this material system to be an ideal candidate for brain inspired electronics.