This paper adds a number of novel concepts into global s/t cut methods improving their efficiency and making them relevant for a wider class of applications in vision where algorithms should ideally run in real-time. Our new Active Cuts (AC) method can effectively use a good approximate solution (initial cut) that is often available in dynamic, hierarchical, and multi-label optimization problems in vision. In many problems AC works faster than the state-of-the-art max-flow methods  even if initial cut is far from the optimal one. Moreover, empirical speed improves several folds when initial cut is spatially close to the optima. Before converging to a global minima, Active Cuts outputs a multitude of intermediate solutions (intermediate cuts) that, for example, can be used be accelerate iterative learning-based methods or to improve visual perception of graph cuts real-time performance when large volumetric data is segmented. Finally, it can also be combined with many previous methods for accelerating graph cuts.