Methods and systems are disclosed for using a chromatic lens system to provide a “flying focus”—i.e., an advanced focusing scheme enabling spatiotemporal control of a focal location. In a method, a photon beam is emitted from a source at a wavelength. The photon beam may have more than one wavelength. The photon beam is focused to a focal location using a chromatic lens system. The focal location is at a first longitudinal distance along an optical axis from the chromatic lens system. The wavelength of the photon beam is changed as a function of time to change the focal location as a function of time. The wavelength may be changed such that the focal location changes with a focal velocity.