Optical imaging through and inside complex samples is a difficult challenge with important applications in many fields. The fundamental problem is that inhomogeneous samples such as biological tissue randomly scatter and diffuse light, preventing the formation of diffraction-limited images. Despite many recent advances, no current method can perform non-invasive imaging in real-time using diffused light. Here, we show that, owing to the ‘memory-effect’ for speckle correlations, a single high-resolution image of the scattered light, captured with a standard camera, encodes sufficient information to image through visually opaque layers and around corners with diffraction-limited resolution. We experimentally demonstrate single-shot imaging through scattering media and around corners using spatially incoherent light and various samples, from white paint to dynamic biological samples. Our single-shot lensless technique is simple, does not require wavefront-shaping nor time-gated or interferometric detection, and is realized here using a camera-phone. It has the potential to enable imaging in currently inaccessible scenarios.