In his first week as President, Donald Trump issued several Executive Orders impacting federal regulations. One executive order froze any proposed or pending regulations, with limited exceptions for "urgent circumstances relating to health, safety, financial, or other national security matters". Another executive order, signed January 30, targets the number of regulations in total, and requires that agencies revoke two regulations for every new one they issue. The order calls on the Office of Management and Budget (OMB) to set a budget for each agency, and requires agencies to control the costs of any new rules within their budget. Any costs associated with new rules would have to be offset by the repeal of at least two existing rules.
Trump criticized the Dodd-Frank Wall Street Reform and Consumer Protection Act, calling it a "disaster". The law created oversight of the regulatory process, promoted transparency, and streamlined agencies through the creation of some new ones, with the merger or elimination of others. Notable new agencies created by Dodd-Frank were the Financial Stability Oversight Council, the Office of Financial Research, and the Bureau of Consumer Financial Protection. President Trump has said that he plans to "[do] a big number on Dodd-Frank".
Though the 2-for-1 order will likely be carried out during any new rulemaking processes, there is ambiguity around how a regulation is defined within the context of the order. A single regulation may deal with multiple sections of the regulatory code; it is unclear whether these would be counted as one regulation or many.
Another question for many is the scope of power than the President has through executive orders to impact regulations. The Hill published an article a little over a year ago that goes through some of the considerations for what can, and what cannot, be done by the President regarding regulations. That article is available here.