What comes next? Oh, nothing much, other than a fractious fight to pick a new Conservative Party leader and prime minister, the October 31 deadline for leaving the European Union on terms still not known, and potentially a general election at some point that will test the coalitions of the Tories and the Labour Party.
The final candidates are put to a postal ballot of the wider Conservative Party membership, with the victor named the new leader.
May's time as prime minister has come to a crashing end over the unrest among her own MPs triggered by the Brexit withdrawal plan which she had planned to announce today.
"I will shortly leave the job that has been the honour of my life to hold", Ms May said.
"From my perspective, I don't see the European Union offering any new prime minister a better or very different deal to what was on offer to Theresa May", Coveney told Ireland's Newstalk radio station after May on Friday said she would quit.
Was it the day President Donald Trump announced his arrival to the United Kingdom with a newspaper interview in which he poured scorn on her Brexit plan, just a few hours before they were due for a joint press conference? "Our politics may be under strain but there is so much that is good about this country".
She said her successor would need to find a consensus in parliament on Brexit.
Business leaders have warned that Theresa May's successor must table an immediate plan to break the Brexit deadlock, amid mounting concern that candidates in the Conservative leadership contest will back a no-deal withdrawal.
The next British leader is likely to be a staunch Brexiteer, who will try to renegotiate the divorce deal, and if that fails to leave the bloc without an agreement on departure terms.
Sterling reversed initial gains it made on Ms May's resignation.
After suffering many humiliations, most recently Conservatives losing more than 1,300 seats in local elections this month, her departure was not unexpected.
The grassroots members who ultimately pick the victor are older and more socially conservative than the party's millions of voters and, beyond that, the wider British public. Her victory came because she was the last person standing, not necessarily the best.
"All prime ministers, in the end, take responsibility for what happens on their watch, but I think that it's undeniable that suddenly and unexpectedly becoming prime minister after the seismic shock of the Brexit referendum meant that she was dealt an extremely hard hand to play", he said. The Conservative and the main opposition Labour parties are expected to fare badly.
Former foreign secretary Boris Johnson, seen as the frontrunner to step into Downing Street, along with Cabinet minister Rory Stewart and former minister Esther McVey have already said they intend to run for the party leadership, while more than a dozen others are believed to be seriously considering entering the contest.
He was one of the co-conveners of the Vote Leave campaign and his pro-Brexit stance should help his cause with the powerful Eurosceptic wing of the Conservatives.
The pound and British stocks rose after news of May's resignation, as some investors appeared to hope it could unblock the political stalemate over Brexit, though analysts warn it could simply mean another delay to the European Union departure. "The EU wants to get on with many, many other challenging political questions", he said.
"I think anybody in her position would have had great difficulty".
The political struggle ahead both within the ruling Conservatives and across the country is likely to be even more brutal than the last two years.