What will happen to dated items and dated material ?

[Umo]

Well by that logic, all of your current gear will be old when 2.0 launches, so you should be completely naked and have to start over.

You shouldn't equal old to dated when talking about FINAL FANTASY XIV and FINAL FANTASY XIV: A Realm Reborn. Dated items come from dated recipes which have been revised and replaced by updated ones with better statistics matching (or supposed to match...) current gameplay. They are supossed to get banished at some point as Yoshi-P / devs have stated (and I'm not going to quote for truth - everyone should do their own homework).
On a side note, I'm not concerned about dated items; I just think that compensating players because of this is pretty weird at best.

[Melinia]

Why? I mean... Hell, why? They are just dated items. Give players a reasonable amount of time for selling/spiritbond them and get rid of them altogether. That's a compensation.
People tend to take these kind of things as if there's no tomorrow... :/

Some of the items can't be replaced. For instance, the old dated precious metal earrings have +Evasion on them, which is impossible to get for that slot now that the old recipes are gone (the new precious metal earrings add Perception instead). Other items simply look better than other gear. For instance, almost all of the hooded robe recipes were removed from the game, making that a much more unusual look.