This is hands down my favorite deck I've ever made.
I've tried many times to get Shirei, Heartless Summoning, and things with etb and death effects to work reliably. This must be the 7th or 8th incarnation of such a deck, but the core is always the same. You start with 4 Heartless Summoning, 4 Mulldrifter, 4 Reveillark, 4 Spellskite, and 3-4x Shirei, Shizo's Caretaker.
The rules regarding the interaction between Shirei and Heartless Summoning is that anything with one or less power comes back at the endstep via Shirei, and Heartless Summoning gives all creatures -1/-1. So really your creatures that are normally 2/2s have are 1/1s that come back at the end step every time they die and your creatures that are normally 1/1s instead have 0 toughness. To further explain that, creatures with 0 toughness do not loop infinitely. They come back once to die immediately and then wait until the next endstep to come back again, hitting the bin every turn as a state-based effect. However this leads to an interesting style of play, which involves winning through stack after stack of card advantage per endstep. This makes the deck play very differently than you might expect... The idea is to rip apart the opponent's board and ability to play with land destruction and bounce, then keep it that way while you slowly win.
The win condition at the moment is not fancy, just attacking with weenies. There are many alternatives though, including Falkenrath Noble, Perilous Myr, Undercity Informant, Laboratory Maniac, Mudbutton Torchrunner, Fallen Ideal, and more. But the win condition isn't actually that important, as if you demonstrate a loop that destroys all their lands or draw more than 3 cards per turn they normally concede.
The high power level of a green based Heartless Shirei has led me to this version, which is also very powerful:
http://www.mtgvault.com/kmk888/decks/heartless-shirei-modern-swarm/
The green is nice for Eternal Witness, Acidic Slime, Treefolk Harbinger, and the swarm master herself, Trostani's Summoner.
It might be easier to explain the rationale for each card instead of all the interactions. So here they are, in order of importance:
Heartless Summoning turns on half your deck. The difference between playing with it and trying to play without it is vast. This is why you play 4 even though you only ever want one on the battlefield, and also why you need 4 Spellskite. You can reanimate the rest of the deck with things like Reveillark, but there is no maindeck way to get this card back if they remove it. This is actually the impetus for splashing green in the green version of this deck (Eternal Witness). If you have it in your opening hand and the ability to produce two mana, you should keep, no matter what the hand is.
MULLDRIFTER. Evoked with Heartless Summoning= 2 cards for one blue mana. With Shirei on the field = 4 cards and a 1/1 body with flying.
Reveillark is the best card in the deck if you're trying to play from behind. He doesn't come back with Shirei but he functions to create card advantage when you can't find Shirei, recuperate from a board wipe, or provide a 4/3 with flying.
Spellskite is the insurance policy. It is necessary to run 4 because every deck in Modern runs some type of disruption and it soaks that up. It also randomly hurts a couple strategies like Bogles and Splinter Twin. Weak to exile effects though. Cartel Aristocrat fixes this.
Shirei is the namesake of the deck, but I have come to realize that he is certainly not the best card in the deck. If you can get Heartless Shirei running without the opponent disrupting it, it will autowin you the game, but this almost never happens and that is the reason the deck has gone through such an evolution over the years. The problem is that for the deck to "go off" usually requires about 4 cards: Heartless Summoning, Shirei, Spellskite, and an accelerant. The reason this deck still exists is that Shirei still contributes to a value based game when the deck doesn't "go off". Quite a few of the creatures in the deck already have 1 or less power, and all of them (except Reveillark) do with Heartless Summoning on the table. So even without the combo, if only one creature dies and comes back to a Shirei trigger, he's probably been worth the mana.
Fulminator Mage and Avalanche Riders are the only reason the deck can even grasp at the Modern format. They're basically the win cons- many decks just have a hard time dealing with land destruction, especially in multiples. Neither card requires a sac outlet to loop with Heartless Shirei, which is nice.
Flamekin Harbinger fetches half the deck and is not dependent on Summoning to work with Shirei. However, putting the card on top instead of into your hand is a big disadvantage. It's still really good though because of the ability to fetch Mulldrifter or Reveillark.
Court Hussar is the best card in the deck to combine with Shirei if you cannot find Heartless Summoning. He will find you that Heartless Summoning or gas, whatever you need. An Anticipate at every end step is almost worth the 8 mana set up.
Nevermaker hits any of the opponent's nonlands, and together with a sac outlet can lock someone out of endgame by nullifying their draw step. It mainly buys time to put Heartless Shirei together... It is important to note is that the main hate against this deck is Torpor Orb and Rest in Peace. This hits both, although it isn't a permanent solution to either.
Solemn Simulacrum is card advantage on a stick.
Cartel Aristocrat is just a sac outlet. I guess Heartless Shirei also makes him undying, but I've still been fairly dissatisfied with him. It's surprisingly hard to find quality sac outlets (since Viscera Seer is a 0/0 with Heartless Summoning in play), so this makes the list. Miren, the Moaning Well is a more expensive but resilient sac outlet included in the main. Blasting Station or Fallen Ideal are alternatives, but Aristocrat comes down earlier. I am hoping that Wizards will soon print a sac outlet that happens to slot well into this deck, especially one that revolves around -1/-1 effects or discard.