Obtain corpse hearts for crafting

Some of the items in the valuables category are used for researching your enemies; these can be turned into the table next to Minaeve - a quest in Haven should show up early on to tell you about this.

A similar table will be in the tower in Skyhold after the Inquisition moves there.

Some of the items in this category are also used for requisitions. Since there's nothing to indicate which valuables are or aren't used in them, and the area requisitions seem to be repeatable infinitely (it just picks another random one from the list for that area each time), it's probably not all that safe to sell any valuables, unless you can get a list of all the requisitions. That said, since the area requisitions only really give Power, you could just ignore them, and only hoard valuables if they're used in another one.

Oh, and of course, there's also the ability to mark items in other categories as valuables, which means basically any item can be in the valuables category. This seems to be intended as a way to mark things for later sale, by hitting Sell All on the valuables category once you get to a shop. This works alright, provided you turn in research first, but only if you don't care about the requisition items being lost.

Take a look in your codex entries for creatures. As you flip through the cards, you'll see black and white pips in the upper right. One pip means you have descriptive text. Two pips means you have an advantage. Scroll to the bottom of the descriptive text to see the advantage you unlocked.

If you've turned in some material for a given creature codex entry, you will also notice a progress bar displayed on the card.