The rest of this site exists to lay out the facts. This page exists to attempt to explain them. It will be up to the courts to determine if the explanations offered here are correct.
What follows is a plausible worst case scenario...
The Trump campaign could have implicitly or explicitly promised Putin that Trump would:
1) Turn his back on NATO and withhold aid from Ukraine
2) Distance the US from European allies, especially German Chancellor Angela Merkel
3) Take the United States out of the Paris accord (Russia is a major oil and gas exporter)
4) Withdraw from trade deals which disadvantage Russia
5) Weaken the US government by fostering political division within the US
6) End the economic sanctions on Russia
Putin could have promised in return to help him win the presidency and help him financially by:
1) Hacking into Democratic Party servers and leaking the results
2) Sending millions of fake news stories about Hillary Clinton to targeted voters
3) Tapping into voter registration databases
4) Helping clear the way to build a Trump Tower in Moscow as well as financing other projects
5) Helping Trump repay his debts to foreign banks
6) Not revealing any incriminating information he may have had on Trump
It would seem likely that, in this scenario the policy concessions would be negotiated by Sessions, Flynn, JD Gordon, and Paul Manafort.
The financial and political benefits recieved in return would likely have been negotiated by Sater, Kushner, Page, and again Manafort. Any actual cooperation between the Russian efforts to influence the election and the Trump campaign seems likely to have gone through Cambridge Analytica and WikiLeaks.
We lay out this explanation so as to be clear about the frightening scenario which seems very possible based on available evidence. That possibility should be enough to motivate Americans to take this issue very seriously, and support investigations. We do not claim that there is definitive proof that this is what happened, at this point. But it is consistent with the evidence we do have and cannot at this point be ruled out.
Below we link to some alternative explanations. The first are the explanations put forward by the Trump campaign and administration members who have been accused of collusion:
Trump lawyers say no income from Russia, with exceptions CBS (May 12th, 2017)
Trump Lawyer ‘Vehemently’ Denies Russian Collusion New York Times (August 30th, 2017)
Jared Kushner's statement on Russia to congressional committees CNN (July 24, 2017)
One year into the FBI's Russia investigation, Mueller is on the Trump money trail by Evan Perez, Pamela Brown and Shimon Prokupecz at CNN (Aug. 3, 2017) (Includes statements by representatives of Carter Page, Roger Stone, Michael Flynn, Paul Manafort, and Donald Trump)
Next some plausible explanations which, while they may involve some wrongdoing, are not as dramatic as the one outlined above.
Seven Theories of the Case: What Do We Really Know about L’Affaire Russe and What Could it All Mean? By Jane Chong, Quinta Jurecic, Benjamin Wittes at Lawfare (May 1, 2017) And Seven Theories of the Case, Updated: One Year Later, What More Do We Know About L’Affaire Russe? by Quinta Jurecic and Benjamin Wittes at Lawfare (Aug. 2, 2018).
The Innocent Explanation, Part #1 by Josh Marshall at Talking Points Memo (March 3, 2017)
Obama’s CIA chief just offered a Trump-Russia quote for the ages by Yochi Dreazen reporting on the testimony of John Brennan at Vox (May 23, 2017)
Trump Jr.’s Russia meeting sure sounds like a Russian intelligence operation by Rolf Mowatt-Larssen at the Washington Post (July 14, 2017)
An ex-CIA officer: the Trump Jr. meeting shows how the Russians exploit intelligence targets by Sean Illing interviewing Glenn Carle at Vox (Jul 14, 2017)
Trump's shady and inept campaign team was a perfect target for Putin's spies by Zack Beauchamp at Vox (Nov 1, 2017)
Was the Trump Campaign Full of Spies or Just Idiots? by Marcy Wheeler for Vice (Feb 26 2018)
What did Trump know, and when did he know it? by Philip Bump at the Washington Post (Feb. 26, 2018) "Was Trump told that the Russians were trying to help him, perhaps even told about specific actions or information, and did nothing?"
Why The Trump/Russia ‘Skeptics’ Are Wrong by Joshua Marshall at Talking Points Memo (Feb. 21, 2018) "Corrupt transactions are often tacit. You’re helping me. I’m helping you. It’s a good thing for both sides. No need to complicate it."
For Russia, Trump Was a Vehicle, Not a Target by Clint Watts for the New York Times (Apr 3, 2018) "In Trump and his campaign, Mr. Putin spotted a golden opportunity — an easily ingratiated celebrity motivated by fame and fortune, a foreign policy novice surrounded by unscreened opportunists open to manipulation and unaware of Russia’s long run game of subversion."
Another explanation has been put forward by a hacker who was tried in Russia for breaking into bank records. He confesses to the DNC hacking under the direction of the FSB, but distances himself from the Kremlin. It is unlikely the confession letter would have been leaked without Kremlin approval.
Putin Ordered Theft of Clinton's Emails from DNC, Russian Hacker Confesses by Cristina Maza at Newsweek (Dec. 12, 2017)
And finally, a couple of more in depth looks at that scariest scenario:
Oh, Wait. Maybe It Was Collusion. By John Sipher and Steve Hall at the New York Times (Aug. 2, 2017)
We’re Back to Manafort by Josh Marshall at Talking Points Memo (Aug. 4th, 2017)
The Art of the (Trump and Putin) Deal by Robert Reich (July 11, 2017)
Putin's Payout: 10 Ways Trump Has Supported Putin's Foreign Policy Agenda by Max Bergmann, James Lamond, and Talia Dessel at the Moscow Project (July 10, 2018)
Russian Leverage Over Trump Is Not Just a Theory. It’s Now Fact by Jonathan Chait (May 8, 2018)
Will Trump Be Meeting With His Counterpart — Or His Handler? A plausible theory of mind-boggling collusion by Jonathan Chait (July 8, 2018)
An Epiphany Article on the Trump/Russia Story by Joshua Marshall at Talking Points Memo (July 10, 2018)
There is Only One Trump Scandal by Adam Serwer (May 21, 2018)