The Republican primary is effectively over, and Donald J. Trump will really, truly be the nominee.

Mr. Trump won Indiana so convincingly on Tuesday that he drove Senator Ted Cruz of Texas, his chief rival, out of the race. One more contender, Gov. John Kasich of Ohio, remains, but for all intents and purposes, the contest is finished.

On the Democratic side, Senator Bernie Sanders’s victory did little to alter the race. Hillary Clinton’s delegate lead remains intact, and Mr. Trump’s emergence as the unchallenged Republican standard-bearer may help the Clinton cause as Democrats grow anxious about the general election matchup.

Here are some of our takeaways from what proved to be a decisive night for the Republican race:

Trump’s problems begin at home

With his victory in Indiana, Mr. Trump inherits a Republican Party that has been traumatized and torn apart by his campaign. A majority of primary voters in the later contests ultimately chose him, but potentially crippling divisions persist on the right: In Indiana, roughly a quarter of Republican voters said they would be scared to see him elected president, according to exit polls.

It is not clear that Mr. Trump has it in him to unite the party. His final day on the campaign trail was a tour de force of political brutality. He first lobbed the outlandish claim that Mr. Cruz’s father had a connection to John F. Kennedy’s killer, and then mocked Mr. Cruz as a floundering loser. Mr. Trump has continued to ridicule other vanquished foes, including Jeb Bush, long after they left the race.