Federal judges have always wielded great influence. But as Congress has failed to pass major legislation in recent years on issues like abortion, immigration and gun ownership, the courts have assumed a more pronounced role, setting the agenda on some of the country’s most divisive questions.

When voters pick the next president, they will also be choosing between two visions of the federal judiciary. Federal judges are nominated by the president and confirmed by the Senate, and almost all will serve for life, shaping American law for generations.

President Biden and former President Donald J. Trump both understood the judiciary’s powerful sway over American life. Mr. Trump succeeded in naming more federal judges in a single term than any president had since Jimmy Carter, and Mr. Biden is close behind.

Today, around half of all federal judges were nominated by one of the two most recent presidents. A New York Times analysis of their choices found stark differences among them in ideology, demographics and prior experience.

The next president will probably take office with roughly 40 vacancies to fill. Many more openings can be expected over the next four years because of deaths, retirements and resignations. And successfully filling those vacancies will largely depend on control of the Senate.