These are some of our most important takeaways from Tuesday’s voting:

Trump is bleeding

When presidential candidates get closer to their party’s nomination, they often gain stature and appear more formidable as they approach the general election. For Mr. Trump, the opposite may be happening.

He is winning, but at a terrible price. The intensifying attacks on his personal character and business record, and the scenes of violence at his rallies, appear to be taking a toll, exit polls show. In no state did a majority of Republican primary voters say they believed he was honest and trustworthy. In every state that voted on Tuesday except for Florida, about two in five Republicans said they would consider voting for a third-party candidate over Mr. Trump and Mrs. Clinton in November.

Clinton is in command

With landslide wins in Florida and Ohio, Mrs. Clinton re-established herself as the prohibitive favorite in the Democratic race. Taking Ohio by double digits, she eased fears that Mr. Sanders might become a breakaway favorite across the Midwest after his upset victory in Michigan last week.

There were no cracks in her base of support with black and Latino voters, or with older Democrats in general.

And voters appear sympathetic to her criticism of Mr. Sanders as a candidate making fantastical promises: In every state on Tuesday, about three-quarters of Democratic primary voters said they considered Mrs. Clinton’s policy proposals realistic, putting her ahead of Mr. Sanders in that category by double digits in every state but Illinois.