what do you do with them?

They can be equipped to certain weapons that have mod slots (Mostly higher end weapons like Godlies and Legendaries). Other than that, they really have no use currently.

You can use them to modify your weapons. Some add an extra icon, some defend an icon, and there are also tears that can increase your weapon's healing percentage.

Only some weapons have mod sockets though (the spots to add tear crystals).

[edit] Lol, I'm slow.