Everyone complains about the lack of good card draw in Modern as a key factor keeping control decks down in the format. What many don't don't realize is that the tempo required to gain card advantage gets punished more harshly in Modern than any other format. In Legacy you can draw cards and then answer your opponent's threats with Force of Will and Daze, but Modern doesn't have free countermagic on that power level.
Ancestral Vision was supposed to be the answer because it requires such a low mana commitment, but the time needed for it to unsuspend has proven to be too prohibitive for it to be a dominant card.
What you really need is a means to draw cards when you have the time to do so, but with the option to play defensively if you're under a lot of pressure. A split card Lightning Bolt / Ancestral Recall would be perfect! It would also be the best card ever printed by a significant margin, so we're going to need to put in some extra work.
Enter Swans of Bryn Argoll.
It's a fine win condition as a four-mana 4/3 flying creature. It gets bonus points for being immune to Abrupt Decay and Lightning Bolt. But in combination with your own Lightning Bolts, you have your mythical Izzet split card. Are you dying to a Wild Nacatl? Get it out of here. Are you relatively safe? Gas up for the low price of one mana.
But we can do better than that. Skred Red just won a Modern Grand Prix, right? Skred is pretty close to Lightning Bolt but becomes a draw four, five, six, seven as the game goes long, which is how you want games to go when you're drawing a bunch of cards for one mana.
Generally you want to complement your card draw with cheap interactive spells, and Izzet has that in spades. Spell Snare, Remand, and Mana Leak are all Modern staples and your card draw spells double as some of the most efficient removal in the format. Of course, Snapcaster Mage is there to give you added access to your spells, and I can't imagine not wanting the fourth.
Notably, Blood Moon functions well in this deck because Snow is a supertype which Blood Moon does not affect, so your Skreds are still effective. The result is a classic U/R Control deck that doesn't need to devote space to card draw spells, which significantly increases your flexibility. That flexibility is really what's missing in Modern control decks because you need it to compete against such a varied metagame.