Requirements
Vessels are Titan-only. Patch summaries say the slot requires maximum Resonance, R6. You craft them with Titan Shards or obtain them from Aberrant-or-higher raids. The equipped Vessel also works in Waves. A Mythic craft is listed at 100 Shards and a Divine craft at 400. Use the shard planner with the number on your craft screen if it differs.
A Vessel does not replace a perk, a Family, or a skill. It changes one part of the Titan you already have.
Divine vessels
Atomic Armageddon is the Colossal burn tool: critical hits against Burn, 15% shorter Colossal wind-ups, Anguish affecting the user, 20% more Heatwave radius, and double Awakening Bar gain.
Impenetrable Shield scales with Shield Strength. Every 10 Shield Strength adds 1% damage, skill cooldown reduction, and movement speed. While Courage is active, every second hit deals 20% bleed. Earth Breaker splits, and hits count twice toward Warrior's Brawn at 1.20 times the buff.
Impure Savior adds Awakening Bar gain against Fear, a second Quakeslam when four or more Titans are hit, faster infectious projectiles that can apply Corrosion, and a stronger Higher Purpose that also hits you.
Primordial Devil is the damage Vessel shown on Attack Titan builds: 20% damage against Burn, Hardening that no longer increases Awakening drain and grants 15% damage, two extra targets on skills during Hardening, and a missing-health bonus to damage and punch speed during Berserk.
Scarlet Blossom is the critical Female-side Vessel: a 20% super-crit chance on crits for 45% super-crit damage, a stronger and wider Roundhouse Kick with 10 seconds off the cooldown, and 25% damage reduction plus 15% less Awakening drain during Crimson Bloom.
Mythic vessels
Brute Force removes heavy-attack endlag, adds 25% heavy damage and crit damage, and forces bosses to drop grabbed players.
Counter Guard lets you block during punch or heavy endlag, opens a 0.5 second parry, and buffs the next three hits by 20% damage, 15% crit damage, and 10% crit chance while resetting block cooldown.
Noxious Blood puts 5 seconds of Corrosion on Titans that hit you and returns 3% health when you hit a Corroded Titan. A separate note says Corrosion makes the target take 20% more damage. That status line is worth confirming in game.
Pugilist removes punch endlag, adds 45% punch damage and 20% punch speed, and makes the Block Bar 25% more effective. It disables all active shifter skills, so it is a punch build, not a skill build.
Thunderous Attunement adds Awakening gain, a short punch-speed buff, and a Shock chance on crits. Shock can hit bosses that are not mid-skill, and it does not stack.
Void's Call makes Roar apply 15 seconds of Fear. Affected bosses lose most skills and cannot regenerate until it ends.
What to craft first
Craft one Mythic that matches a problem you already feel: Noxious Blood for sustain, Brute Force for heavies, Counter Guard if you can parry, Void's Call if the raid is a single boss. Spend 400 Shards on a Divine only when you will keep that Titan. Colossal players look at Atomic Armageddon or Primordial Devil. Armored players look at Impenetrable Shield. Female players look at Scarlet Blossom. Beast players are pointed at Noxious Blood in current vessel guides because the form trades in longer hits.