Cutting a section from an image.

I want to cut (or copy) a section from an image on my artboard, but I can't see to find a way to do it.  For example, in Microsoft paint I can use the select tool to draw a rectangle around part of the image and Copy or Cut that selection into the clipboard and paste it back.

I know I can cut this out and paste it onto an Artboard, but I am curious about the capability in Illustrator.  Thank you for your help.