What is the capital of Switzerland?

Switzerland is a federation of cantons that were careful not to let any one of them become dominant, and the missing capital is part of that design.

Federal city, not capital

The Swiss constitution says nothing about a capital. What exists instead is the Bundesstadt, the federal city, a status Bern was given by a decision of the Federal Assembly in 1848 and which has never been written into the constitution since. The word used is deliberate.

Bern was chosen over Zürich and Lucerne partly because it was bilingual German and French, partly because it was central, and partly because it was not Zürich.

Where the federal institutions actually are

Spreading the courts across the language regions was a decision of the same kind: the judiciary was moved out of Bern in 1874 and has never been brought back.

What to say

Bern, in practice, and most sources including this one record it as the capital. If precision matters, in a legal document or a constitutional question, the accurate phrase is "federal city".

Switzerland is not the only country whose capital is a title rather than an address; see the Netherlands and Bolivia.