Supported Metal Organic Frameworks (MOFs) with a high specific surface area are of great interest for applications in gas storage, separation, sensing, and catalysis. In the present work we report the synthesis of a novel composite architecture of MOF materials supported on a flexible mat of electrospun nanofibers. The system, based on three-dimensional interwoven nanofibers, was designed by using a low-cost and scalable multistep synthesis protocol involving a combination of electrospinning and low-temperature atomic layer deposition of oxide materials, and their subsequent solvothermal conversion under either conventional or microwave-assisted heating. This highly versatile approach allows the production of different types of supported MOF crystals with controlled sizes, morphology, orientation and high accessibility.