Rescue, or Search and Recovery Divers do quite a bit. We will do water rescues, search for drowning victims, and recover objects from underwater; that could be anything from the size of a dump trunk to a person, to a weapon of some type. The scope of what you do depends on your training, the parent organization, whether it is fire or law based, and what else is available in the area. Our team is fire based but we respond to scenes for the local law enforcement agencies as well.
This is not something you can just go through a recreational scuba class and decide to do one day. There is a myriad of laws, rules, and regulations to contend with. Most scenes are considered to be HazMat scenes on way or another, if you have a vehicle in the water your scene is contaminated with petroleum based contaminates, if you are recovering a body you have biological contamination just for example.
You need to be extremely confident in your skills as a scuba diver to the point that they are second nature before even thinking about proceeding to this level. 99.99999% of the time you will be working by feel, in zero visibility, by yourself, in a HazMat scene. This is a extremely hazardous endeavor even with proper training, and done correctly following all applicable rules and regulations. Anything less is just suicide.
If you have any specific questions I will do my best to answer.