The mystery at the core of the Trump-Russia story is motive.

President Trump certainly seems to have a strange case of Russophilia. He has surrounded himself with aides who have Russian ties. Those aides were talking to Russian agents during the campaign, and some are now pushing a dubious peace deal in Ukraine. Trump recently went so far as to equate the United States and Vladimir Putin’s murderous regime.

But why?

It’s not a simple question. In their Russia-related inquiries, the F.B.I. and the Senate Intelligence Committee will need to focus first on what happened — whether Trump’s team broke any laws and whether the president has lied about it. Yet the investigators, as well as the journalists doing such good work reporting this story, should also keep in mind the why of the matter. It will help explain the rest of the story.

The United States has never had a situation quite like this. Other countries have tried to intervene in our affairs before, sometimes with modest success. Britain and Nazi Germany, for example, tried to influence the 1940 presidential election, financing bogus polls and efforts to sway the nominating conventions. But never has a president had such murky ties to a foreign government as hostile as Putin’s.

I count five possible explanations for Trump’s Russophilia, and they’re not mutually exclusive.

The first is the justification that Trump himself gives, and you shouldn’t dismiss it simply because he has an open relationship with reality. He says that fewer tensions with Russia would benefit the United States, which is a reasonable position. It’s not so different from the position of John Kerry, President Barack Obama’s secretary of state.