When sunspots rotate onto the solar disk facing Earth they are identified by their structure in white or visible light. Sunspots are regions of concentrated magnetic field. They are like complicated clusters of bar magnets on their sides. Some are just like a single or simple bar magnet and some are very non-uniform and complicated. The more complex they are the more magnetic energy they contain and the higher chance they have to erupt releasing energy by events such as solar flares and coronal mass ejections. Like bar magnets on their sides the sunspots have loops of magnetic field coming up from the visible solar atmosphere called the surface or photosphere and going back down into the surface. Magnetic fields are not visible but these loops are traced by hot solar plasma that is visible in more energetic wavelengths of light such as extreme ultraviolet (EUV) or X-rays.
Here is a video of composite SDO/AIA/HMI 171 angstrom images and white light (visible) images for 2 weeks (from 00:00:00 on Nov. 1, 2013 to 23:59:59 on Nov. 14, 2013.) When the sunspots are on the solar disk they are shown rotating and changing as they move from left to right (East to West) across the sun in the white light SDO/HMI images. When the sunspots are not visible just before they rotate into view or just after they rotate out of view we can see the magnetic loops rising up from them in the SDO/AIA 171 angstrom EUV light.