The chuck is around the shoulder and neck of the cattle. It works well when it is cooked slowly. Flat iron steaks and chuck roasts are especially popular meats to have here.
The round is around the back part of the cattle and is a little fattier than other parts. It is roasted and dehydrated in many cases to create a fresh quality meat. It is tough in that it is hard to cut through unless you have something very sharp to work with. Even so, it can produce a great rump roast when prepared right.
The brisket is on the lower part of the cattle and is right underneath the chuck. It is often tough because it has lots of connective tissue. This is one of the best cuts of beef for barbecuing as it can come apart well when heated properly.
Another popular choice for barbecue needs, the ribs include great cuts that contain the best quality meats in most cases. Prime rib and rib-eye steaks are often prepared from this area. The meats here are tender and have plenty of juice to create a strong flavor all the way around.
The flank is a long cut that comes off of the abdominal muscles on the livestock. This is one of the toughest cuts of beef and as a result works best when braised. It works especially well in a London broil to create a good texture all the way around.
The loin is a part of the cow that comes from the back area right behind the ribs. It is often grilled as the key is to keep it dry. The T-bone steak is the most prominent thing you can get out of the loin.
All these options for cuts of beef are great worth looking into. Contact a gourmet butcher to see what you can get out of such meats.