Do Fish Sleep?

Fish do not sleep in the same way that humans do.  In fact they cannot close their eyes, so they will never 'look' asleep.  However, they do have periods when they need to rest and perhaps doze gently.  They do not fall into a deep sleep, even a very gentle ripple in the water will be sufficient to wake them up.  
When a fish is resting it often moves its fins.  This actually keeps them balanced in the water, but their bodies are resting and on a 'go slow' similar to other animals when asleep.  Other than the fins moving, the fish will be very still and docile.
Some fish choose to sleep at the bottom of the ocean.  This affords them more protection from predators.  Most fish will rest on their stomachs, but some, like the triggerfish which rests on the ocean floor, will lie on thier sides.   Some fish, such as the slippery dick which is found in Australia, will bury themselves in the sand when resting, so that they cannot be seen.