Many Democrats and some Republicans said the scandal-plagued Ken Paxton’s victory could turn Texas into a battleground state that will determine Senate control.

© Desiree Rios for The New York Times

Republican voters made a familiar bet, that Texas is conservative enough that any Republican, even the most conservative, will beat a Democrat.

© Desiree Rios for The New York Times

James Talarico, the Democratic nominee for U.S. Senate, has been raising money and looking to unite his party for the general election.

© Tamir Kalifa for The New York Times

President Trump has sought revenge in G.O.P. primaries. Democrats have turned out to vote in large numbers. Republicans have gained a redistricting advantage.

© Meridith Kohut for The New York Times