"What do you study at university?"

Translation: Was studierst du?

[LSadun]

Where did "at university" go? Is university-level study implied by "studieren"?

[Paralars1]

studieren = to study at university / to be a university student.
It can also mean to carefully examine

Ich studiere Chinesisch = I study Chinese as a degree

Ich studiere. = I am a university student

Ich studiere die Zeitung = I am thoroughly reading the newspaper

If you want to use study in the non-university conext, use "lernen"

[MortiBiRD]

You will encounter many people that say Ich studiere but they do not study at a university, they study at a Fachhochschule. So I would not agree entirely with you.

[AbunPang]

True, “to pursue higher (tertiary) education” would be more exact ;)

[rjjacob]

My German relatives would ask me, "Was studierst du bei der Uni?"