Abstract: The explosive increase in digital communication of the Big Data and Internet of Thing era spurs the development of universal memory that can run at a high speed with high density and nonvolatile storage capability, as well as demonstrates superior mechanical flexibility for wearable applications. Among various candidates for the next generation information storage technology, resistive switching memories distinguish themselves with low power consumption, excellent down-scaling potential, large scale 3D stacking ability and CMOS-compatibility, fulfilling the key requirements for high performance data storage. In addition, employing organic and hybrid switching media allows light weight and flexible integration of molecules with tunable device performance via molecular design-cum-synthesis strategy. In this review, we try to present a timely and comprehensive review of the recent progress in organic and hybrid resistive switching materials and devices, with particular attention on their designing principle for electronic properties tuning and flexible memory performance. The current challenges posed on the development of organic and hybrid resistive switching material and flexible memory devices, together with their future perspectives, are also discussed.