A compact electronic device may include a camera module having an image sensor. The image sensor may be controlled by storage and processing circuitry to capture image data from received light. The camera module may include a substrate having front and rear surfaces. The image sensor may be mounted to the rear surface of the substrate. The substrate may include optical focusing structures on the front surface of the substrate that focus light through an opening in the substrate to the image sensor. A flex circuit may be used to convey signals between the camera module and other electronic device components. The flex circuit may be mounted to the front surface of the camera module substrate to help reduce total height of the camera module. The flex circuit may be mounted to an extended portion of the substrate or may be mounted to surround the periphery of the image sensor.