Very little is likely to actually happen immediately on May 8 if US President Donald J. Trump does not renew sanctions waivers for Iran.
Indeed, there is only one waiver scheduled for renewal by a May 12 deadline. That provision is Section 1245 of the 2012 National Defense Authorization Act (NDAA).
Section 1245 had a much larger impact on Iran than most other statutory provisions levied by the United States between 2010 and 2016. It was ostensibly a banking sanction, requiring the president to prohibit the opening of correspondent or payable-through accounts by a foreign financial institution (FFI) the president determined to have knowingly conducted or facilitated any significant financial transaction with the Central Bank of Iran or another designated Iranian financial institution—or to impose strict conditions on the maintenance of such accounts.
By itself, this would have been a crippling threat to many foreign governments buying Iranian oil, because Iran required them to pay for oil deliveries through the Central Bank of Iran.