尽管 + [clause],但(是) / 可是 + [clause]
尽管 + [clause],[subject] + 还是 / 仍然 / 也 / 却 + [predicate]
[clause],尽管 + [clause]
尽管 opens a clause stating a fact that you'd expect to get in the way, and the next clause says what happened anyway: "even though", "despite". The second clause carries a turning word – 但是, 可是, 还是, 仍然 or 却.
English allows "although" or "but", never both. A Chinese 尽管 sentence wants the second half marked too, with 但是 or with an adverb like 还是 after the subject. Leaving it out makes the sentence sound cut off.
They do the same job and take the same partners. 尽管 is a little stronger, closer to "even though" or "despite", and it often goes with 还是 or 仍然 for something done in the face of an obstacle. 虽然 is the everyday choice for a plain contrast.
A 尽管 clause can follow the main clause as an afterthought. Then nothing marks the first half.
尽管 straight before a verb in an offer, as in 有问题尽管问 "feel free to ask", is a different use, covered in its own point. As "although", 尽管 heads a whole clause.