The interactions with touchscreens rely heavily on vision: The virtual buttons and virtual sliders on a touchscreen provide no mechanical sense of the object they seek to represent. This work presents PopTouch: a 500 mu m thick flexible haptic display that creates pressable physical buttons on demand. PopTouch can be mounted directly on touchscreens or any other smooth surface, flat, or curved. The buttons of PopTouch are independently controlled hydraulically amplified electrostatic zipping taxels (tactile pixels) that generate 1.5 mm of out of plane displacement. When pressed by the user, the buttons provide intuitive mechanical feedback thanks to a snap-through characteristic in their force-displacement profile. The snap-through threshold can be as high as 4 N, and is tuned by design and actuation parameters. This work presents two versions of PopTouch: a transparent PopTouch for integration on Touchscreens with built-in touch sensing, such as smartphones and a sensorized PopTouch, with embedded thin-film piezoelectric sensors on each taxel, for integration on substrates without built-in touch sensing, such as a steering wheel. PopTouch adds static and vibrating button-like haptics to any device thanks to its thin profile, flexibility, low power consumption (6 mW per button), rapid refresh rate (2 Hz), and freely configured array format.|PopTouch is a submillimeter thick reconfigurable haptic display of pressable buttons. The array of individually controlled electrostatically driven buttons adds an intuitive user interface to any smooth surface (flat or curved). Both a fully transparent PopTouch (for flat panel displays) and a sensorized version are reported, adding haptics to the back of a phone, a steering wheel and an OLED touchscreen.image