[Beef Filet; Filet de Boeuf (French)]
This is a "premium cut", from which restaurants derive many of their most profitable (and fancily named) dishes. It is taken from the loin area, inside the ribs and just below the spine near the aft end of the beef, just forward of the "round" (the beef's tush). This muscle is very lean, but gets less exercise than any other muscle in the beef, so it is naturally tender. It also has the least beefy flavor, making it suitable for showing off the chef's sauces.
The photo specimen is cut IMPS/NAMP #190A, full tenderloin with all fat and side muscle removed. Note the "wing", the crosswise piece at the right end (the iliacus muscle) is not included in the classic recipes but cut away for some other use. The thick end (to the right) is the aft end and called the "butt" end. This specimen was 25 inches long, 1-1/4 inches thick and up to 3-1/2 inches wide, not counting the "wing". It weighed 2.46 pounds, about average,
More on Cuts of Beef.
Buying: Mail order houses sell USDA Prime cuts from the tenderloin for up to 2009 US $80.00 / pound (usually shipped frozen). Some experts consider "Prime" a waste of money for this already tender cut and are perfectly happy with "Choice", and even "Select" wouldn't be bad. Supermarkets sell Choice for between $14 and $20 per pound. Discount warehouses are reported to sell at under $10, but that's for IMPS/NAMPA #189 (no A) which means they haven't had the fat layer removed. To compare to #189A prices you have to multiply the warehouse cost by 1.5 and then figure your labor.
The ethnic markets I normally shop at sell tenderloin at the butcher's counter for between 2009 US $4.79 and $5.99 per pound, but the U.S. grown photo specimen was from the floor cases at an Asian market in Alhambra. It was still in the shrink wrap as shipped from the meat packer. The price was $2.99 / pound, and the USDA grade was probably "Standard", since there was no visible fat in the meat and it was sold without a USDA grade. Flavor was quite good though, and the meat decently tender. Keep in mind the USDA grade indicates nothing more than the amount of fat marbled through the meat. Select and Standard are leaner and Prime is very fatty (only about 2% of American beef is fatty enough to rate Prime).
Which cut number you buy (see next section) depends on usage. Unfortunately your local market will not have their cuts conveniently identified by number, but you should be able to figure it out from the descriptions below.
The #189 will cut into steaks (#1189) with a surround of fat which you can trim to the thickness you desire. The #189A steaks (#1189A) will have very little fat, but more than the #1190, and will be a bit larger because the side muscle is still on. These two cuts are fine for simpler recipes. The #190/190A cuts are best for the more refined recipes and will have just about no external fat at all, but they will be smaller. These cuts are desired by fancy chefs so the fat doesn't interfere with the taste and texture of their sauces.
Prep: The preparation effort depends on the cut number you have purchased and your intended use. It can range from removing fat and silver skin to just making a few cuts. For the classic cuts you will remove the "wing" so the tenderloin looks like the diagram below. Reserve the wing for other uses.
#189 needs all the external fat removed, but most of this usually
pulls off easily by hand. Then remove the "silver skin", the membrane
around part of the main muscle. I've found this is easy to pull off in
shreds once you cut it free at one end.
French practice is a bit more formal. While American butchers tend to call
the entire tenderloin "Filets Mignons", the French reserve
Filets Mignons for only a few slices at the small end of the filet de
boeuf. Beyond that you
have Tournedos, then Chateaubriand for the thicker center
section and finally Biftek at the tet de filet, the big
Cooking: Because of their small size Tournedos and other cross cuts of tenderloin are presented two to a serving. They are generally cut 1-1/2 inches thick or a little more and weigh between 3 and 4 ounces. They may be tied around with string to hold their shape. Also, because this cut is so lean, a strip of bacon may be wrapped around before tying with string. Tournedos are just about always served with sauces (a different sauce for each of the two in fancier restaurants).
Tenderloin should not be cooked harder than medium rare, or you're just wasting your money. If you want "well done", fry hamburgers.