The advantages of compact fluorescents are they are energy efficient, compact in size, have good lumen maintenance, long life, endless shapes and sizes, dimmable, easy retrofit, low operating cost, and radiate less heat.
Compact Fluorescent bulbs are about 4 times as efficient as incandescent bulbs. A typical 13w compact fluorescent bub will emit the same amount of light as a 60w incandescent.
They are relatively small in size for the light they emit. Most CFLs about 4-5 inches tall with the larger, super high output CFLs measuring about 12 inches tall. This makes them excellent bulbs for retrofits and almost any type of lighting application.
They have good lumen maintenance means their light output does not depreciate very much over their life time. Even after a couple of years of usage a CFL will be almost as bright as day one. This is not the case for HID metal halide or high pressure sodium bulbs which can depreciate by as much as 50%.
Their average life is about 10,000 hours compared to only an average of 2000 hours for incandescent and 50,000 hours for LEDs.
Their many shapes and sizes also makes them excellent bulbs for many types of lights. They are tubular shapes for chandeliers, flood shape CFLs for recessed downlights and uplighting floods as well as standard A-shape and globe replacements. There is hardly a socket that cannot be fit with a compact fluorescent bulb.
Many newer CFLs are dimmable. Be sure the CFL is marked dimmable and check for dimmer compatibility before purchase.