How to build a control Warlock?

[Protato]

How does one go about building a control-based Warlock? Spells, invocations, that sort of thing. OLooking at things like the Grasp of Hadar, Warlocks have more options than before for controlling combat. I haven't looked over the Celestial Warlock but the Hexblade doesn't seem to offer much control versus the Archfey or Fiend.

[Zanthy1]

The obvious invocations are the ones like Grasp of Hadar and Repelling Blast (10ft towards or away from you). Personally I'd essentially throw in any invocation that works with eldritch blast, but also get spells like hunger of hadar for some area shut down

[Spiritchaser]

Chains of Carceri is worth discussing. It’s either incredibly good or totally irrelevant. It comes late but... If you’re a level 15 chain look I can’t see not taking it.

I wouldn’t underestimate the ground and pound available from eldritch smite

Repelling blast has been discussed, it’s good, easy, and you probably have it already...

[Joe the Rat]

You've got some options, but choose wisely - you are going to lack some depth. Most of what you have is going to be specific direct/individual control, or control-by-coercion (penalties for entering zones)

Invocations:
Grasp and Repel are incredibly potent, if for no other reason than there's no saves. You hit, you push. Add Lance of Lethargy, and one of the 1-4 things you shot at also -10 for movement.
You also have several one-a-day curse-like options here (Mire the Mind, Bewitching Whispers, Dreadful Word, or Sign of Ill Omen for actual curses), but the rest is going to be more creativity than control - Misty Visions for illusory disruptions, or Sculptor of Flesh for the occasional newting. Maddening Hex is an interesting one, as it encourages your enemies to space out, or suffer a penalty. But pass on this unless you are Hexblade, as you will likely be using concentration on not-hex.

Spells:
Hunger of Hadar is my go-to for area control. It doesn't stop movement, but it slows, and punishes. HoH and Repelling Blast to play reverse-goalie is a time-honored Warlock strategy.

For more precise (or less environmentally distruptive) options, you also get Crown of Madness, Hold Person (and Hold Monster), Hypnotic Pattern, and the Penultimate Penalty Box: Banishment.

The Arcanum give you a few more options - Dominate Monster, Demiplane, and Forcecage, for example. But this is pretty late-game.

Patrons:
Archfey: are really about the team game - you add faerie fire (less control, more support), plant growth (custom made double-difficult terrain), dominate beast, dominate person.
Fiend: Does not add much. Command is an early, easy tweak on action, and Stinking Cloud gives you a horrendously debilitating (but not damaging) zone of Nope, but one that nonbreathers and unpoisonables can ignore. That might be something to consider if you have a lot of Yuan Ti or Dwarven allies.
Old One: Here you go. Tasha's laughter prones and essentially incapacitates a target, the Archfey dominations, plus Everybody's Favorite Black Tentacles.
Undying: Doesn't bring anything to the table... other than contagion. But that's almost the reverse of control.
Hexblade: Not so much. Most of the oomph here is on single-target.
Celestial: Do you like cleric control spells? Because they get cleric control spells.

My recommendation: Focus on blast-shifting - possibly all four blast-related invocations. You could set aside agonizing if you are okay focused on control rather than damage. For area options, pick a variety of saves: HoH for Dex-avoid damage, and hypnotic pattern (or the various holds) for Wisdom saves.