New Applications of Network Flow
Network flow has been used for all sorts of interesting and surprising tasks in computer vision and image processing.  For instance, it has been used for image segmentation, image stitching, seam carving, image denoising, stereo image correspondence, and more.

See, e.g., https://en.wikipedia.org/wiki/Graph_cuts_in_computer_vision, What&#39;s the relationship of max-flow-min-cut and Markov Random Fields?, https://cs.stackexchange.com/a/37423/755, https://en.wikipedia.org/wiki/Image_segmentation#Graph_partitioning_methods