My commentary will be brief, since I'm not at all an expert in any field related to this. Maybe Flee can hop in, but I don't believe it's been discussed here.

Article I, Section 9, of the Constitution contains what is known as the Foreign Emoluments Clause, which reads, “no Person holding any Office of Profit or Trust under them, shall, without the Consent of the Congress, accept of any present, Emolument, Office, or Title, of any kind whatever, from any King, Prince, or foreign State.” An emolument is defined by Merriam-Webster as “the returns arising from office or employment usually in the form of compensation or perquisites.”

http://blog.constitutioncenter.org/2017/01/trump-addresses-emoluments-clause-but-will-it-be-enough/

tl;dr Trump owns businesses all over the world and any profits generated by foreign governments at those businesses may be considered a 'present' or 'Emolument'. Without consent from Congress, this is unconstitutional, and the Left are making a very large stink about Trump supposedly violating the constitution immediately upon swearing in. A few examples of upcoming potential conflicts to this clause include:

For example, the Kuwait National Day celebration, thrown by the Kuwaiti embassy, will be held at Trump’s downtown D.C. hotel in February.
The Industrial and Commercial Bank of China Ltd. (ICBC), which is controlled by the Chinese state, is currently paying rent for tenancy in the Manhattan Trump Tower (according to mortgage documents filed in 2012, it is the Tower’s largest office resident).
And, for some foreign politicians and foreign diplomats in town for the inauguration, Trump’s Washington hotel is the place to be this weekend, according to reporting from the New York Times.
Each of these represents an incident in which the President of the United States will, effectively, be receiving payment from a foreign government.

https://thinkprogress.org/trump-constitution-first-day-office-55d1f0668c27#.dx24cnf9d

So what has Trump done?

“Just like with conflicts of interests, he wants to do more than what the Constitution requires,” Dillon said. “President-elect Trump has decided and we are announcing today that he is going to voluntarily donate all profits from foreign government payments made to his hotels to the United States Treasury.”

Dillon also explained that that Trump is having his two oldest sons run his company during his time in the White House.  His oldest daughter, Ivanka, will also have no connection to the company. Recent federal election documents show that Trump has financial interests in more than 500 domestic and foreign firms.

Trump’s assets will be placed into a type of trust that isn’t a blind trust, since it will be partially managed by his sons, but it will “completely isolate him from the management of the company,” Dillon said.

Trump’s company won’t start any new deals abroad and all domestic deals will be subject to an approval process, Dillon added. A new ethics officer will also join the company to be involved in a vetting process. She also explained that a complete liquidation of Trump’s assets into a blind trust would cause more potential conflicts. “President-elect Trump should not be expected to destroy the company he built,” Dillon said.

http://blog.constitutioncenter.org/2017/01/trump-addresses-emoluments-clause-but-will-it-be-enough/

However,

Dillon’s claim is, at the least, debatable among experts of government ethics.

"If any of Trump’s business arrangements involve the receipt of payments from foreign governments, I believe that he, or his entities from which he receives money, would have to forgo those payments, or he would have to detach from those entities," Kathleen Clark, an expert on legal ethics and a law professor at Washington University in St. Louis, previously told us.

Trump, noted above, has said he will resign from the Trump Organization.

http://www.politifact.com/truth-o-meter/article/2017/jan/11/live-coverage-donald-trumps-first-press-conference/

In short, Trump is donating these profits to the treasury, and divesting himself of his businesses by handing control over to his sons and vowing to stay isolated from their dealings. Worst case, Congress will have to establish a committee that tracks and approves these emoluments as they occur, which is probably very tedious, but Constitutional.

Thoughts on this issue?

http://money.cnn.com/2017/01/20/news/trump-conflicts-inauguration/index.html

Another interesting potential conflict involving a hotel Trump owns in D.C., technically he can just turn the deed over to his son since the paperwork only says it has to be owned by a non-official.