Large-area nanopatterning technology has demonstrated high potential which can significantly enhance the performance of a variety of devices and products such as LEDs, solar cells, hard disk drives, laser diodes, wafer-level optics, etc. But various existing patterning technologies cannot well meet industrial-level application requirements in term of high resolution, high throughput, low cost, large patterned areas, and the ability to pattern on non-ideal surfaces or waters. Soft UV-nanoimprint lithography (UV-NIL) by using a flexible mold has been proven to be a cost-effective mass production method for patterning large-area structures up to wafer-level (300 mm) in the micrometer and nanometer scale, fabricating complex 3-D micro/nano structures, especially making large-area patterns on the non-planar surfaces even curved substrates at low-cost and with high throughput. In particular, it provides an ideal solution and a powerful tool for mass producing micro/nanostructures over large areas at low cost for the applications in compound semiconductor optoelectronics and nanophotonic devices, especially for LED patterning. That opens the way for many applications not previously conceptualized or economically feasible. The flexible mold is the most critical elements for soft UV-NIL. The performance of the flexible mold has a decisive effect on the soft UV-NIL in term of resolution, patterning area, throughput, uniformity of the imprinted patterns, and repeatability of multi-imprinting. The key enabler that can fulfill mass production of micro-and nanostructures over large areas by NIL is the continual advancement of mold techniques (structures, materials and fabrication processes) towards higher resolution over a larger area at a lower cost. This paper provides a comprehensive review on the structural types, materials used and fabrication methods of various flexible molds in soft UV-NIL, surveys major progress in various flexible molds, particularly highlights some concluding remarks and generalizations. Two key issues for flexible molds, deformation mechanism and controlling solution of soft molds as well as fabrication of large area (wafer level) master template, are described in detail. Furthermore, prospects, challenges and future directions for flexible molds are addressed. Finally, some potential or promising solutions for improving the performance of flexible molds and soft UV-NIL process, as well as some important conclusions are presented.