With the inside curves more or less in place, the next thing to do is to get rid of all of the wood on the outside that isn't part of the violin. A ledge is put in around the edges of the plates; this can be done by hand, or very easily using an abrasive bit on a drill press (Yay power tools!)
This ledge will be where the purfling--the black-and-white-strips of inlaid wood--will be placed. It also helps to set a limit on how far the wood should be removed. With the ledge in place, it's time to get out the big gouges and the flex-shaft tool with the kutzall bit, and just get rid of wood.
The closer to finished you get, the more delicate tools you must use: from kutzall to big gouge to small gouge to thumb planes.
From this, the next step is purfling, which is very, very exciting.