Materials that can expand and collapse, fold, and transform into a variety of shapes have attracted significant interest and have applications in the design of flexible electronics, color displays, smart windows, actuators, sensors, and both photonic and phononic devices. But how can we render a rigid device super-flexible so that it can wrap around a sphere without bending and stretching? How can flat surfaces be transformed into any desired three-dimensional (3D) structure without disruptive or catastrophic deformation? The key lies in cuts. Here, we review recent research progress in the design of super-conformable and foldable materials by employing fractal cutting and lattice-based kirigami elements that combine cutting and folding. By prescribing cuts with different motifs, identifying edges in the right geometry, and by programming the folding directions, we show that a single flat sheet can be transformed into a variety of targeted 2D and 3D structures—a pluripotent platform for new technologies.