Jeskai Control is a modern archetype as old as the format itself. It aims to stop the opponent from executing their plan with a suite of counterspells and removal, prolonging the game until it can overwhelm the opponent either by going bigger or through card advantage. Next to a solid core of efficient cards, Jeskai Control leaves a lot of room for customisation, mostly in the way and at what time in the game the deck aims to win; because of this, a plethora of subtypes of the deck has developed. Which version you end up choosing depends on your metagame and personal preferences.
Out of all the different color combinations to choose from when playing control in Modern, why choose Jeskai? The main advantage of Jeskai lies in its versatility and ability to switch gears in the middle of an ongoing game. This is primarily because of jeskai's powerful burn suite of Lightning Bolt, Lightning Helix and Electrolyze. Although removal spells like Path to Exile, Fatal Push and Terminate are less conditional removal than burn, choosing the desired amount to run can be difficult due to how wide the Modern metagame tends to be; with a removal suite wide enough to battle Modern aggro decks, you will be left with a large amount of dead draws in creaturelight matchups, and might even find yourself with too few cards to side in postboard. Jeskai on the other hand can turn those dead removal spells into a clock, and suddenly change from a controlling position into the aggressor; "end of turn, bolt snap bolt" followed by an attack puts your opponent 8 life points lower seemingly out of nowhere.
Commonly played cards
As jeskai is mostly a "goodstuff" archetype, relying more on individual card strength than synergistic interactions, there is a lot of variation in decklist depending on metagame and personal preference. A major factor in this lies in how the list intends to finish the game and on what turn it intends to do so.
Having access to this card is basically the main reason to play blue in Modern. Snapcaster is an immensely mana efficient card advantage machine, most of the time flashing back the best spell in your graveyard to counter or kill one of your opponent's spells, and leaving a 2/1 body behind that either trades with a block or removal spell or comes in for a bunch of damage. Snapcaster is arguably at his best in the Jeskai shell, as the access to both card draw and burn makes you able to play the card as aggressively as you want; hold onto it until you need your best graveyard spell, flash back an Opt or Serum Visions to apply some pressure without losing a card, or go pedal to the metal with an "end of turn, bolt snap bolt".
Clique provides hand disruption for blue, an effect generally reserved for black. Furthermore, its 3/1 body becomes a dangerous thread with burn backup. Together with Narset, Parter of Veils, this becomes a clean Thoughtseize on a stick if played in their draw step.
Spell Queller is seen in the more midrange builds of Jeskai, or as a sideboard card for matchups where we want to be the aggressor. Its 2/3 body blocks surprisingly well against several decks, and it can apply pressure against combo and ramp decks whilst also disrupting their setup. The card does require some finesse, as it dying at the wrong time can prove disastrous. With the addition of Teferi, Time Raveler, this card got even better.
Restoration Angel can re-use the abilties of the above mentioned creatures, as well as providing a 3.4 flying body that often lines up very well in the meta, both offensively and defensively.
Geist of Saint Traft
Geist ends games real quick. Midrange decks can be built around him, and control decks can use him in the sideboard to pivot into a much faster gameplan.
One of the most efficient removal spells in Modern. Although the downside is not free, especially early in the game, Path to Exile stops virtually any creature and also stops recursion and death triggers, of which there are many in Modern.
Access to bolt is one of the things that gives Jeskai its extreme versatility, being both an excellent removal spell as a way to close out the game.
The lifegain on this card is incredibly relevant and can help stabilize against aggro decks; especially against Burn, this card is a 2 for 1 most of the time. Next to that it is bolt number 5+, and you want some amount in any type of jeskai list, mostly dependant on how reliant you are on burn to the face. In more controlling builds, Lightning Helix is sometimes preferred over Lightning Bolt
With Ponder and Preordain banned, SV is the most powerful cantrip in Modern. Scry 2 is excellent in any phase of the game, helping with hitting landdrops, finding answers, planning turns and out-topdecking in the lategame. If you play it, you generally play the full playset...
...unless you play Opt. Although obviously weaker than Serum Visions in raw power, Opt's instant speed puts real pressure on your opponent to play into your countermagic, because if they don't use their mana, you can Opt and/or Snap Opt end of turn to gain tempo and free pressure.
Although expensive for a removal spell, Electrolyze gives excellent value and is a 2 for 1 or even a 3 for 1 against Modern's swarm decks, like affinity and Collected Company-based decks. In grindy games like the mirror, Electrolyze can be used to deal direct damage without losing a card, making it an excellent card to "test the waters" and provoke a response with. As the addition of the War of the Spark Planeswalkers have filled up the 3 mana slot for UWx decks in modern, this card has fallen out of favour a bit, but it is still a consideration.
The face of Modern Control. Cryptic Command is never dead in your hand, it's like a Swiss army knife. Although it is incredibly powerful and often a 2 for 1, 1UUU is expensive and clunky to cast, especially in counter wars. The amount you want to run varies from 0 to 4 depending on your manabase, manacurve and how long you want the game to go.
As WotC refuses to give us Counterspell in Modern, Logic Knot is probably the next best thing. Its power over Mana Leak is that it stays relevant even late in the game, when you might have to counter for x=4 or higher. The card is more color intensive than Mana Leak and makes you more sensitive to gravehate however, so it is not all upside. Generally, 2 or 3 are played, although some pilots prefer Mana leak and/or Remand over it.
As most creature decks in modern make counterspells poor in some way or another, opting out of countering creature spells for more upside is often a good idea. The addition of Veto changed blue mirrors immensely.
Force of Negation
Modern's Force of Will is not as versatile as its Legacy counterpart, but will still save you from being killed by Modern's many quick combo decks.
Generally the wrath of choice in Modern. Jeskai has so much spot removal, wrath effects aren't even that necessary, but having one or two mainboard can still be a good safety valve for more controlling builds.
Jace,the Mind Sculptor
The infamous Boogyman is finally Modern legal. Not as busted as once feared, but a fine addition nonetheless. With 3 starting loyalty he is very fragile, but with two or three activations he puts us so far ahead he tends to end the game on his own. Learning how to Brainstorm properly is fundamental to using Jace.
Teferi, Hero of Dominaria/card]
Just like Jace, big Teferi closes the game real quick. Although his card advantage is not as devastating as Jace's, his higher starting loyalty and untap effect make him much easier to protect.
[card]Narset, Parter of Veils
Narset looks decent until you compare her to Divination, after which she looks absurdly powerful. At the worst, Narset draws you a good card and gains you some life. At the best, Narset draws you two good cards and severely hampers your opponent's gameplan if they are built around card draw effects.
Teferi, Time Raveler
Just like Narset the power of little Teferi is that his "worst case scenario" is still very good. Bouncing something, drawing a card and gaining some life as he dies is fair for 3 mana. The ceiling on little Teferi is winning any counterspell matchup on the spot
Nahiri, the Harbinger
Fallen out of favour but my personal pet card, Nahiri puts a lot of pressure on the opponent by threathening to ult and attack with Emrakul, the Aeons Torn to end the game on the spot. Together with a way to filter through dead cards and an exile effect, Nahiri might not be as devastating as the other mentioned planeswalkers but is a fine choice for anyone who doesn't like to play for 10+ turns every match.