As accusations swirled Sunday about Russia’s efforts to interfere with the 2020 election, President Trump’s national security adviser and former Vice President Joseph R. Biden Jr. could not agree on what Moscow is, or is not, doing.

Their disagreement came as intelligence officials disputed reports that emerged last week about a briefing of the House Intelligence Committee. The officials now maintain that the House members either misheard or misinterpreted a key part of the briefing, and that the Office of the Director of National Intelligence did not mean to say that it believes the Russians are currently intervening in the election explicitly to help President Trump.

America’s global campaign to prevent its closest allies from using Huawei, the Chinese telecom giant, in the next generation of wireless networks has largely failed, with foreign leaders publicly rebuffing the United States argument that the firm poses an unmanageable security threat.

The Trump administration has begun to put a price tag on its growing arms race with Russia and China, and the early numbers indicate that restoring nuclear weapons to a central role in American military strategy will cost tens of billions of dollars over the next decade.

The Israeli-Palestinian peace plan unveiled by President Trump and Prime Minister Benjamin Netanyahu sounds more like a road map for their own futures than for the Middle East.

When Secretary of State Mike Pompeo, in a curse-laden tirade to a reporter on Friday, asked, “Do you think Americans care about Ukraine?” he was getting at an essential element of President Trump’s defense in the impeachment trial. White House officials are convinced that Americans are indifferent to what happens in the struggling former Soviet republic, and they may well be right.

The six Democratic presidential candidates who debated Tuesday night in Des Moines agreed on one point: President Trump threw away a nuclear deal that was working and is now recklessly speeding toward war with Iran.

President Trump opened a small window for diplomacy with Iran on Wednesday, but combined his words with bald threats that made it hard to see how the two countries could break out of their cycle of confrontation and revenge.

Rudolph W. Giuliani, the former New York mayor at the center of the impeachment investigation into the conduct of Ukraine policy, makes a living selling cybersecurity advice through his companies. President Trump even named him the administration’s first informal “cybersecurity adviser.”

The last two impeachment investigations of the past half-century began with a third-rate burglary and an extramarital affair. They quickly expanded to question the credibility and ethics of the president, but never touched on America’s national interests in the weightiest geopolitical confrontations of their eras.

President Trump is pushing Boris Johnson, the incoming prime minister of Britain, toward a hard break with the European Union. But Mr. Johnson could be constrained.