
gefallen
to please
To be liked by someone or to be perceived as pleasant. The person who likes something is in the dative.
Mir gefällt deine neue Frisur sehr gut.
Your new hairstyle really pleases me.
to please / to fall
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to please
To be liked by someone or to be perceived as pleasant. The person who likes something is in the dative.
Mir gefällt deine neue Frisur sehr gut.
Your new hairstyle really pleases me.

to fall in battle
To be killed in combat or war. This is a formal and euphemistic way of speaking.
Auf dem Denkmal stehen die Namen der im Ersten Weltkrieg gefallenen Soldaten.
The names of the soldiers who fell in the First World War are written on the memorial.

to put up with
To accept or tolerate something negative or unpleasant without objecting.
Eine solche unfaire Kritik musst du dir nicht gefallen lassen.
You don't have to put up with such unfair criticism.

to revel in
To enjoy and display a particular role or behavior, often with a vain or self-satisfied connotation.
Er gefällt sich in der Rolle des geheimnisvollen Unbekannten.
He revels in the role of the mysterious stranger.
The verb 'gefallen' (to please, to fall) is inseparable. The prefix 'ge-' remains firmly attached to the verb stem 'fallen' in all conjugated forms and sentence positions.
Er gefiel sich schon immer in der Rolle des Anführers.
He had always reveled in the role of the leader.
In the most common meaning, the person who likes something is in the dative, and the thing that is liked is in the nominative. So the sentence structure is the reverse of the English formulation 'I like it'.
Das neue Album der Band gefällt mir sehr.
The band's new album really pleases me.
In the meaning 'to die in battle', 'gefallen' (to fall in battle) is used almost only in military or historical contexts. It is a formal and euphemistic paraphrase for 'sterben' (to die).
Sein Großvater ist im Zweiten Weltkrieg gefallen.
His grandfather fell in the Second World War.
The idiom 'sich (Dativ) etwas (Akkusativ) gefallen lassen' (to put up with something) means to tolerate negative treatment. Pay attention to the fixed structure with the reflexive pronoun in the dative and the verb 'lassen' (to let).
Lass dir sein unhöfliches Verhalten nicht gefallen!
Don't put up with his rude behavior!
The expression 'sich in etwas (Dativ) gefallen' (to revel in something) describes that someone visibly enjoys a role or behavior. The preposition 'in' is fixed with the verb here.
Sie gefällt sich in ihrer Rolle als strenge Chefin.
She revels in her role as the strict boss.
to look forward / to be pleased
„Gefallen“ describes something that seems pleasant to someone or is liked by them. „Freuen“, by contrast, refers to the joy that something causes someone, often a piece of news or an event. Use „gefallen“ for a positive opinion and „freuen“ for the joy someone feels.

Die neue Gestaltung gefällt mir sehr.
I really like the new design.
Die gute Nachricht freut mich sehr.
The good news makes me very happy.