Photograpy under water can be a great challenge. Here we will discuss photograpy in aquariums as the use of cameras under water is a very specialised field requiring specialised and expensive equipment.
When photographing in aquariums the biggest danger is reflections from the glass sides of the aquarium. It is best to be at an angle to the side of the aquarium, less than 90 degrees, so that you do not get a reflection of yourself directly back from the glass. Also check for reflections of other people as they move around. If using flash for illumination ensure that the flash does not reflect back directly into the lens, hold it at an angle of around 40 degrees.
The glass walls of aquariums are quite often of poor optical quality and generally not so clean, so you will loose some contrast in the image, this can be rectified by giving the image a boost to its contrast in Photoshop in post processing.