One method of cooling that's commonly overlooked (no doubt in part because of how
counter-intuitive it seems) is refrigeration with light. Ordinarily we think of light adding to the
temperature of whatever absorbs it, like the difference between shade and sunlight on a warm day. Even a perfect mirror would only stay the same temperature; while it wouldn't get any warmer it wouldn't get any colder either. Physically this kind of heating makes sense too --
photons hitting a surface that aren't immediately reflected instead excite electrons in the material, jostling its atoms and making the material
hotter.
In fluorescence, photons of a particular wavelength are able to excite the electron to a higher state. After losing some energy in that state, they fall back to the previous state and emit a photon of lower wavelength than was absorbed. That energy loss is why ultra high-frequency black light can make some materials glow in much more visible (i.e., lower frequency) colors. Most materials release very little light, only that of some set of wavelengths, which look like a specific color to us. The rest is converted to thermal energy, heating the material. Even materials that release many photons at a different wavelength, such as the Day-Glo plus black light example above, convert some of the photon energy to heat. As a group, these properties are called Stokes luminescence, and apply to virtually every substance on earth.
Only recently have manufacturing processes become good enough to create a material that displays just the opposite, anti-Stokes luminescence. In this type of luminescence, the photons are absorbed as usual, but the electron is further excited by heat. When the electron eventually jumps back to the un-excited state, a photon is released with greater energy than the one which was absorbed, and heat is lost from the system. Almost magically, the material glows dimmer -- or at least at a shorter wavelength -- than the laser and becomes cooler. This luminescence is very fragile; any contaminants in the material will absorb energy rather than releasing it, counteracting the cooling effect. Sensitivity of these ultra-pure materials to light is also specific, so a laser tuned to precisely the right wavelength must be used.
Notably, optical refrigeration was used in to cool the Bose-Einstein condensates that have been making news since 1995. Hopes are also high for a process that creates pure enough silicon (and a tight enough laser) that this method can be used to extend Moore's Law a few more years. Cooler still (Hah!) is research being done to find a target material cheap enough to manufacture that it could replace the pressure-based systems used in home refrigerators, air conditioners, etc. Besides the near-100% energy efficiency, this would be silent with no moving parts.