
bändigen
to tame
To tame a wild animal or bring it under control.
Der Dompteur versuchte, den Löwen zu bändigen.
The animal trainer tried to tame the lion.
to tame / control
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to tame
To tame a wild animal or bring it under control.
Der Dompteur versuchte, den Löwen zu bändigen.
The animal trainer tried to tame the lion.

to control
To bring something powerful or chaotic under control, for example a force of nature, strong emotions, or a crowd of people.
Die Feuerwehrleute kämpften darum, die Flammen zu bändigen.
The firefighters struggled to control the flames.

to control oneself
To master and keep one's own strong feelings or impulses under control.
Er musste sich bändigen, um nicht wütend loszuschreien.
He had to control himself so as not to shout angrily.
The verb 'bändigen' (to tame/control) is related to 'das Band' (ribbon/band) and 'binden' (to bind/tie). The literal idea is to symbolically put a band around something wild or chaotic in order to control it.
Es war unmöglich, die tobende Menschenmenge zu bändigen.
It was impossible to control the raging crowd.
'Bändigen' (to tame/control) is always used with an accusative object. You ask: whom or what are you taming/controlling? This also applies to the reflexive form 'sich bändigen' (to control oneself), where the reflexive pronoun is the accusative object.
Der Reiter konnte das scheue Pferd nur mit Mühe bändigen.
The rider could only tame the skittish horse with difficulty.
'Bändigen' (to tame/control) is a rather strong and vivid word. It is often used in contexts involving great force or intense chaos, and can therefore sound somewhat elevated or dramatic.
Die Regierung versucht, die Inflation zu bändigen.
The government is trying to control inflation.
In its figurative meaning, 'bändigen' (to control) is often used for forces of nature ('das Feuer' — fire, 'eine Flut' — a flood), strong emotions ('die Wut' — anger, 'die Leidenschaft' — passion), or even something everyday like unruly hair.
Mit diesem Gel kann ich endlich meine Haare bändigen.
With this gel, I can finally control my hair.
to check / control
Kontrollieren can mean keeping a crowd orderly and under your control. Bändigen is especially appropriate when the crowd is chaotic, puts up strong resistance, and must actively be subdued. Without such resistance, kontrollieren is usually the more neutral choice.

Die Ordner bändigen die plötzlich drängende Menschenmenge mit großer Mühe.
The ushers struggle to bring the suddenly surging crowd under control.
Die Ordner kontrollieren die ruhig wartende Menschenmenge mit klaren Absperrungen.
The ushers control the calmly waiting crowd with clearly marked barriers.