とはいえ

とはいえ means "admittedly X, but…": it grants that the first half is true, then says something that goes against what you would expect from it. It goes after the plain form; a noun or な-adjective takes it with or without だ.

At the start of a sentence

とはいえ can also open a new sentence and point back at the one before it, like "still" or "even so".

Register

とはいえ belongs to writing, speeches and careful talk. In conversation the same concession is とはいって言っても or といって言っても, or simply けど. とはいう言うものの means the same as とはいえ and is just as formal.

The second half has to cut against the first. When it merely adds to it, use a plain "and" or "so" instead: ×安いとはいえ、たくさん買った.