とはいえ

1. 1Although / even though X is the case, Y (which runs contrary to the expectation raised by X).Ex. 1
2. 2Granted that X, one still should not take it lightly; it concedes a mitigating fact and then states a caution or judgment.Ex. 2
3. 3As a sentence-initial conjunction (とはいえ、…): that said, even so.Ex. 3

This is a written, fairly formal concessive used in essays, articles, and considered speech. The speaker grants that X is true, then points out a contrary reality or adds a caution. Compared with everyday concessives such as といっても or けど, it sounds more measured and literary. It often appears in general statements, judgments, and advice.

• 1.
  とはいうもののN1「とはいうものの」is basically the same as 「とはいえ」in meaning, attachment, and sentence-initial use, and the two are mostly interchangeable. It carries a quotative nuance from 「と言う」and is less concise than 「とはいえ」, and its following clause generally does not take commands or requests.
• 2.
  といってもN3「といっても」is common in both spoken and written language and has a more casual tone; the following sentence usually corrects the degree or content of the previous one and lowers the listener's expectations, as in 'just everyday conversation'. Both can serve as sentence-initial conjunctions and are interchangeable when limiting degree, but 「とはいえ」is preferable in formal settings.
• 3.
  もののN2「ものの」also marks a contrast after acknowledging an established fact, but its following clause is usually a result that did not develop as expected, carrying regret or resignation; it generally does not take volitional, command, or request forms, requires 「である＋ものの」after nouns, and cannot stand alone at the start of a sentence.
• 4.
  といえどもN1「といえども」is more solemn and stiff; its first clause is often a status, extreme condition, or smallest amount, and its second clause is often prohibition, obligation, or negation. When acknowledging a fact mid-sentence and then contrasting, the two are mostly interchangeable, but 「といえども」cannot be placed at the start of a sentence as a conjunction.
• 5.
  にしてもN2「にしても」also expresses concession and is interchangeable with 「とはいえ」when the first clause is a fact; however, it can also attach to hypotheticals and has the parallel usage 「AにしてもBにしても」, with a neutral register, and 「だ」cannot follow nouns or な-adjectives.

とはいうものの is nearly synonymous but slightly heavier. といっても is more colloquial and often downplays what was just said, while ものの attaches directly without と. といえども is more literary and often stresses even an extreme case, and にしても can also express hypothetical concession ('even if') in a more conversational tone.