In terms of Zilean, he's an underpicked champion which is weird because he's never really been nerfed hard enough for it to matter. Zilean used to be picked and banned in many tournament matches back in season 1. However, the mid metagame has shifted towards champions like Morgana, Karthus, Anivia, and Ryze: champions that exhibit hard CC, have more DPS, or have a stronger late game than Zilean (usually more than 2 of the 3 previously mentioned characteristics). However, that doesn't necessarily mean that Zilean's bad though, it just means that he's not picked. Utility AP champions like Orianna and Morgana are still picked, so Zilean can very well be picked also. Zilean's ultimate is still one of the strongest in the game because no other one has the reviving capability like it does (except Yorick but we're talking about mid lane). Sometimes you'll see Zilean be played as support, which can work, but it leaves his two abilities that scale off of AP to be sadly left in the dust. Furthermore, this guide is not about support Zilean, but rather AP mid Zilean.
Mainly, you play Zilean because you hate seeing your teammates die. He has powerful poking capability and great movement for both yourself and your team. However, he falls off late game to be little more than an "ult bot", so make sure that you take advantage of his powerful midgame along with your teammates.
Amúgy ez olyan szépen leírja zileant, hogy én sem tudnám szebben.