Most monocular depth sensing methods use conventionally captured images that are created without considering scene content. In contrast, animal eyes have fast mechanical motions, called saccades, that control how the scene is imaged by the fovea, where resolution is highest. In this paper, we present the SaccadeCam framework for adaptively distributing resolution onto regions of interest in the scene. Our algorithm for adaptive resolution is a self-supervised network and we demonstrate results for end-to-end learning for monocular depth estimation. We also show preliminary results with a real SaccadeCam hardware prototype.