Congratulatory Telegram After Trump’s Election Mr. Putin was one of the first world leaders to congratulate Mr. Trump on his victory in the 2016 election, with a note Mr. Trump later described as “beautiful.”

First Phone Call Mr. Putin and Mr. Trump spoke for the first time, by phone. The two men agreed “on the absolutely unsatisfactory state of bilateral relations” between the United States and Russia, according to a statement from the Kremlin. Trump’s office said the president-elect “noted to President Putin that he is very much looking forward to having a strong and enduring relationship with Russia and the people of Russia.”

Trump Releases Christmas Greetings From Putin Mr. Trump’s office released a translated holiday letter from Mr. Putin expressing a wish for cooperation and collaboration. “A very nice letter from Vladimir Putin; his thoughts are so correct,” Mr. Trump said in a statement.

Congratulatory Call After Trump Takes Office Several of Mr. Trump’s senior advisers were present in the Oval Office for his first phone call with Mr. Putin as president. Jonathan Ernst/Reuters Mr. Trump received a congratulatory phone call from Mr. Putin that lasted about an hour.

Phone Call After St. Petersburg Attack Mr. Trump called Mr. Putin to express his condolences for the victims of a terrorist attack on the subway in St. Petersburg.

Phone Call on Syria The two presidents spoke by phone about the war in Syria, terrorism in the Middle East and North Korea.

Private Discussion at G-20 Meeting in Hamburg, Germany Stephen Crowley/The New York Times Mr. Trump and Mr. Putin met face to face for the first time on the sidelines of the Group of 20 economic summit meeting, along with Rex W. Tillerson, the secretary of state at the time, and Sergey V. Lavrov, the Russian foreign minister. According to a former senior administration official, after the meeting Mr. Trump took away his interpreter’s notes and told the interpreter not to discuss the conversation.

Second Discussion at G-20 Meeting in Hamburg It was later reported that Mr. Trump and Mr. Putin spoke again at a dinner for G-20 leaders, joined only by Mr. Putin’s translator. The dinner was closed to reporters, and the White House did not publicly disclose the conversation until it was reported more than a week later. There is no official United States government record of what was said.

Brief Conversations at Asia-Pacific Economic Cooperation Meeting in Da Nang, Vietnam The White House said no formal meeting would occur between Mr. Trump and Mr. Putin at the forum, but video showed the two presidents shaking hands and chatting. Mr. Trump later said he asked Mr. Putin about Russian meddling in the 2016 election and that Mr. Putin denied it. “Every time he sees me he says, ‘I didn’t do that,’ and I really believe that when he tells me that, he means it,” Mr. Trump told reporters. “I think he is very insulted by it, which is not a good thing for our country.”

Hourlong Phone Call The two presidents spoke on the phone about terrorism, Syria and Ukraine.

Phone Call After Putin’s Annual News Conference Mr. Trump thanked Mr. Putin for acknowledging the United States’ strong economic performance. They also discussed North Korea, according to the White House.

Phone Call on St. Petersburg Terrorist Plot Mr. Putin called Mr. Trump to thank United States intelligence agencies for providing information that he said helped to foil a terrorist plot in St. Petersburg, Russia.

New Year’s Letter From Putin Mr. Putin sent Mr. Trump well wishes for the new year and called for “pragmatic cooperation” between their two countries.

Phone Call After Moscow Plane Crash After a plane crash in Russia killed 71 people, Mr. Trump spoke to Mr. Putin to express his condolences.

Phone Call After Putin’s Re-election Mr. Trump called Mr. Putin and congratulated the Russian president on his election victory, confounding aides who wrote clear instructions on briefing materials: “DO NOT CONGRATULATE.”

Two-Hour Private Meeting in Helsinki, Finland Doug Mills/The New York Times After a preliminary meeting that included other American officials, Mr. Trump met with Mr. Putin privately in their first formal summit meeting, accompanied only by their interpreters. The White House provided scant information about what was said, leaving even some administration officials in the dark. At a joint news conference afterward, Mr. Trump avoided criticizing Mr. Putin and questioned his own intelligence agencies’ conclusion that Russia interfered in the 2016 election. Democrats have called on Mr. Trump’s interpreters to testify about this meeting and others.

Informal Conversation at G-20 Meeting in Buenos Aires Juan Mabromata/Agence France-Presse — Getty Images Mr. Trump abruptly canceled a planned meeting with Mr. Putin, citing concerns about Russian aggression toward Ukraine. Mr. Trump appeared to avoid Mr. Putin, even as they posed for a photograph together with other world leaders. But the two men eventually held a brief, “informal” conversation over dinner with other world leaders that evening, according to the White House. The dinner was closed to reporters.