
aufgreifen
to take up
To notice an idea, thought, topic, or suggestion and pursue it further or respond to it.
Ich möchte den Punkt aufgreifen, den Sie vorhin erwähnt haben.
I would like to take up the point you mentioned earlier.
to take up / pick up
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to take up
To notice an idea, thought, topic, or suggestion and pursue it further or respond to it.
Ich möchte den Punkt aufgreifen, den Sie vorhin erwähnt haben.
I would like to take up the point you mentioned earlier.

to pick up
To find and arrest or take a person into custody, usually by the police.
Die Polizei konnte die entflohenen Häftlinge nach kurzer Zeit wieder aufgreifen.
The police were able to pick up the escaped prisoners again after a short time.

to pick up
To pick something up from the ground or from a surface.
Sie bückte sich, um die heruntergefallene Münze aufzugreifen.
She bent down to pick up the coin that had fallen.
'Aufgreifen' (to take up/pick up) is a separable verb. The prefix 'auf-' stands at the end in a main clause. In a subordinate clause, the verb stays together, and in the infinitive with 'zu', 'zu' goes in the middle.
Der Journalist griff das Thema in seinem Artikel auf.
The journalist took up the topic in his article.
The verb consists of the prefix 'auf-' and the verb 'greifen' (to grab). The literal meaning, 'to reach up and take,' helps you understand the abstract meanings too: you 'take up' an idea or a person.
Können wir diesen Punkt später noch einmal aufgreifen?
Can we take up this point again later?
In the abstract meaning, 'aufgreifen' (to take up) is often combined with words from the area of communication and ideas. Typical phrases are: ein Thema aufgreifen (to take up a topic), eine Frage aufgreifen (to take up a question), einen Gedanken aufgreifen (to take up a thought), or eine Anregung aufgreifen (to take up a suggestion).
Die Rednerin griff eine Frage aus dem Publikum auf.
The speaker took up a question from the audience.
When 'aufgreifen' (to pick up) has a person as its object, it almost always refers to a police or official context. It then means to find a person and take them along or arrest them.
Ein Spaziergänger fand das vermisste Kind und die Polizei griff es auf.
A walker found the missing child, and the police picked the child up.
to record / take in
To resume a discussion means to continue it after an interruption. To aufgreifen a suggestion or thought, on the other hand, means to respond to it and pursue it further. Aufnehmen therefore focuses on the interrupted activity, while aufgreifen focuses on a specific piece of content.

Nach einem Einwand greift die Leiterin den Vorschlag auf und prüft ihn genauer.
After an objection, the manager takes up the proposal and examines it more closely.
Nach der Pause nimmt die Leiterin die Diskussion über den Vorschlag wieder auf.
After the break, the manager resumes the discussion about the proposal.