Mrs May said her new-look government now "looks more like the country it serves" following the promotion of a raft of female and ethnic minority MPs.
Scottish Tory leader Ruth Davidson tweeted: "Sorry to see @JustineGreening leave government - she brought her non-nonsense, northern accountant's eye to every brief and is a real role model for LGBT+ Conservatives". However, this is slightly lower than under Cameron, when 50% of minister went to Oxbridge.
His resignation came a day after the prime minister had defended the journalist and free school supporter in the role amid doubts over his lack of education experience and criticism of past comments on social media. Although he has a low profile in the party and media but, according to his government biography, he previously "spent 18 years working in the pubs, brewing and hotel industries, in Britain and overseas". Instead, Esther McVey becomes Work and Pensions Secretary. She has quickly bounced back into a cabinet-level job after losing her seat in 2015 and then parachuting into a safe constituency previous year.
The health secretary Jeremy Hunt, under pressure over a winter NHS crisis, refused to budge when he was asked to become business secretary, which is effectively a demotion.
Transport Secretary Mr Grayling was kept on at his department despite widespread reports that he faced the axe.
Greening was succeeded as Education Secretary by Damian Hinds, who was promoted from being a junior Work and Pensions Minister.
She has installed a fellow Remainer, David Lidington, as de facto deputy prime minister after her last Remainer deputy Damian Green left under a cloud.
Former work and pensions secretary David Gauke has taken over the roles of Lord Chancellor and Justice Secretary vacated by Mr Lidington.
For the second time in her calamitous premiership the Prime Minister attempted to assert her authority, and for the second time she was slapped down.
James Cleverly, a prominent backbencher, is the new Tory Party deputy chairman.
China Trade Cools As Imports Fall Short But Exports Rise 11%
In December, China's exports jumped 10.9% from a year ago to $231.8 billion, down from a 12.3% pace in the previous month. Prices were around 5,500 yuan (US$848.44) per tonne this week, off 45% from peaks seen in late December.
In an official statement, DUP leader Arlene Foster said Brokenshire had "immersed himself fully in the role [of Northern Ireland secretary] by dedicating long hours to trying to make progress".
Mary Bousted, joint general secretary of the NEU teaching union, said: "Just when positive things are starting to happen, to have her moved and the Department for Education in turmoil again would not be good for education".
Digital minister Matt Hancock takes over from his old boss as Culture Secretary. He has been a minister at DCMS.
As well as an over-representation of private school alumni, nearly half - 48% - of Cabinet ministers went to either Oxford or Cambridge universities.
Brandon Lewis also took over from Sir Patrick McLoughlin as Conservative Party chairman during the shake-up on Monday.
James Brokenshire steps down as Northern Ireland Secretary for health reasons.
Mrs May was forced to apologise "unreservedly" after attacking the absence of shadow education secretary Angela Rayner.
And Chief Secretary to the Treasury Liz Truss also stays in post.
Similarly, Philip Hammond, whose first budget ended in a humiliating u-turn for the Tories over National Insurance rates, keeps his hands on the national finances.
Penny Mordaunt remains in post as International Development Secretary. Home Secretary Amber Rudd was also appointed by May as Minister of Women and Equalities.