The Constitution mentions only two crimes by name: treason and bribery. They come up in the clause about grounds for impeaching a president. Apparently the founding folks were especially worried about these because they might induce the president to take actions bad for the country. Federal law codifies the criminality of the latter in the Foreign Gifts and Decorations Act, which states that any gift to a federal official, including the president, worth more than $415 is the property of the United States and not of the recipient. If a foreign leader gives the president a soccer ball autographed by his country's best player, that's probably all right—unless the player is really famous and the ball is worth over $415, in which case it goes to the National Archives.
Donald Trump had a lot of trouble with the concept that expensive gifts from foreign leaders—for example, a $7,000 set of golf clubs from the Japanese Prime Minister—unfortunately weren't his to keep and had to be turned over to the Archives. It has now come out that while president, Trump and his family accepted (and failed to report and turn over) many gifts from foreign leaders. As another example, Saudi Arabia gave Trump 17 unreported gifts valued at $48,000, including a $24,000 dagger from Mohammed bin Salman, just in case Trump needed to kill a pesky reporter and cut him up (sometimes the snark gets very dark around here). Some recent detective work shows that while president Trump and his family received 117 foreign gifts that he did not report and that they were worth roughly $291,000. As usual, it is all about the grift.
Rep. Jamie Raskin (D-MD), the ranking member of the House Oversight Committee, suggested that these gifts violate the Constitution's Emoluments Clause. He urged Congress to pass a law that would define foreign emoluments more precisely and make receiving them a federal felony as well as an impeachable offense. House Republicans know that such a law would first hit Joe Biden and thus they should be for it, but they also know that if they eliminated the opportunities for grift, Donald Trump might drop out of the presidential race and they certainly don't want that. (V)