The primary election in Texas on Tuesday was among the most expensive and hard-fought in state history, as factions of the Republican Party battled for control.

It was in large part a referendum on the fate of moderate Republicans in the Texas House, which impeached the Republican attorney general and blocked some hard-right priorities last year.

And as in other parts of the country, many of those Republicans fell on Tuesday to challengers who were more stridently partisan and aligned with former President Donald J. Trump.

While key races like that of the Texas House speaker were heading for a runoff, Tuesday’s vote underscored the enduring power of the Republican base to punish party incumbents seen as insufficiently conservative.

“They are Republicans who said they were conservative and then they didn’t keep their word to the voters,” Lt. Gov. Dan Patrick, who backed several challengers, said in an interview late Tuesday in Orange, Texas.

“The Band-Aid is now off,” he added. “From now on, they will be held accountable for their votes.”

Here are four themes that emerged on Tuesday.