Apparatus, methods, and systems provide focusing, focus-adjusting, and sensing. In some approaches, the focus-adjusting includes providing an extended depth of focus greater than a nominal depth of focus. In some approaches the focusing includes negatively-refractive focusing that provides an interior focusing region with an axial magnification substantially greater than one or substantially less than one. In some approaches the focusing and/or focus-adjusting includes focusing and/or focus-adjusting with a transformation medium, where the transformation medium may include an artificially-structured material such as a metamaterial.