The battle for control of Congress was front and center on Tuesday night, with races taking shape in several intensely contested House seats in California and New Jersey. But there were revealing elections in the Midwest and the South, too, underscoring President Trump’s power in the Republican Party and the different ways Democrats hope to loosen his hold on red-state America.

Here are some of our takeaways:

Money matters in California

National Democrats spent over $7 million in an effort to ensure they had a candidate reach the general election in three House districts in California held by Republicans. Their decision to not take their chances in the state’s “top two” system — in which the top finishers in nonpartisan, open primaries face each other in November — appears to have been a wise investment.

The party’s intervention in the districts held by Representative Dana Rohrabacher, Ed Royce and Darrell Issa, all Republicans, paid off: they angered some of their own activists but were virtually certain to advance candidates in each of the three districts, including their preferred picks against Mr. Rohrabacher and in Mr. Royce’s seat.

And the Democrats also got a bit of a lesson about the risks of not intervening, in the race for the seat held by Representative Jeff Denham. The Democrat Josh Harder got little outside help and appeared poised to barely edge out a little-known Republican challenger because the other five Democrats split more than 30 percent of the vote.