The new prime minister will have to manage extracting the country from the E.U., which he promised to finish by the Oct. 31 deadline, with or without a deal. But Mr. Johnson will face the same circumstances that brought down Mrs. May: deep divisions within the Conservative Party, which governs Parliament with a tenuous majority, as well as fierce opposition from other parties to a no-deal Brexit. Here’s how events could unfold.

Mr. Johnson will also have to confront Iran over its seizure last week of a British-flagged oil tanker, which could draw Britain into a larger showdown between Tehran and Washington. Iran’s foreign minister, Mohammad Javad Zarif, warned that Tehran would protect itself.

Perspective: President Trump is pushing Mr. Johnson to break Britain from the E.U. Our correspondents write that while Mr. Johnson is cut from Trumpian cloth, he could be constrained by the complexities of British politics and his establishment background.

Side note: The rise of Mr. Johnson has upended the rules of what leadership should look like, writes our fashion critic Vanessa Friedman. He is also bringing an unsettled domestic situation to 10 Downing Street as Britain’s first single leader in more than 40 years.