The common terms for those are "sand vein" for the digestive tract on the back and "blood vein" for the nerve tract on the bottom. The blood vein usually is only a problem with very large shrimp and sometimes not even then. If it's visible, it can be removed by getting the tip of a knife blade under it. If you buy shrimp with the heads on, with practice, you can pull the heads off (not cut) and take the veins out with it.
This is very much a personal thing. Obviously, those of use who peel our own boiled shrimp don't worry about the veins. Nor do those of us who are able to get them so fresh as to eat them virtually alive.
I mostly get fresh brown Gulf shrimp in Large size and remove only the sand vein, along with the shell. A slick little tool splits the shell and gets the vein.
"Kitchen duty is awarded only to those of manifest excellence..." - The Master, Dogen