The core of the charges:

Senator Chuck Schumer, the majority leader, called on Mr. Menendez to resign minutes after the verdict was read. New Jersey’s Democratic governor, Philip D. Murphy, also said Mr. Menendez should step down and said that he would make a temporary appointment to fill the seat should it become vacant.

Speaking to reporters outside the courtroom, Mr. Menendez said he was “deeply disappointed” and vowed to appeal the verdict. “I’ve never been anything but a patriot of my country and for my country,” he said.

The jury, which spent about 12 hours deliberating, also returned guilty verdicts against two businessmen accused of bribing the senator, Fred Daibes and Wael Hana.

Sentencing in the case was set for Oct. 29. Several of the counts carry terms as long as 20 years in prison.

Here’s what to know:

• The core of the charges: Prosecutors accused Mr. Menendez and his wife, Nadine Menendez, of orchestrating a bribery scheme while he was the Democratic leader of the Senate Foreign Relations Committee. The government contended that the senator acted as an agent of Egypt and interceded to quash criminal prosecutions in New Jersey in exchange for the payoffs and then sought to cover it up.

• Dueling views of the case: In his closing argument, Paul M. Monteleoni, a federal prosecutor, portrayed Mr. Menendez as the mastermind of the plot. “It wasn’t enough for him to be one of the most powerful people in Washington,” he said. “But he also wanted to use it to pile up riches for himself and his wife.”

  In his own summary remarks, Adam Fee, a lawyer for Mr. Menendez, insisted that the senator’s actions had actually been “100 percent appropriate” and accused the government of using “half-truths” to fill in key gaps in the evidence. Mr. Fee also argued that the cash and gold had not been bribes but generous gifts to Ms. Menendez in “lean times.”

• The other defendants: Mr. Menendez stood trial alongside Mr. Daibes and Mr. Hana, who were charged with bribing him. A third co-defendant pleaded guilty and testified that he had bribed the Menendezes with a Mercedes-Benz.

• The senator’s wife: Nadine Menendez was also charged. But her trial was postponed indefinitely while she undergoes treatment for cancer and she did not show up in court.

• A historic prosecution: Mr. Menendez’s storied political career had absorbed a near-lethal blow thanks to the gravity of the charges. Mr. Menendez was the first senator to be charged with acting as a foreign agent, and the first in the Senate’s 235-year history to be indicted in separate bribery cases. (His first prosecution ended in a mistrial in 2017.)