Dominique Strauss-Kahn has succumbed to the inevitable and resigned. Here is his letter to the IMF:

It is with infinite sadness that I feel compelled today to present to the Executive Board my resignation from my post of Managing Director of the IMF.

I think at this time first of my wife – whom I love more than anything – of my children, of my family, of my friends.

I think also of my colleagues at the Fund; together we have accomplished such great things over the last three years and more.

To all, I want to say that I deny with the greatest possible firmness all of the allegations that have been made against me.

I want to protect this institution which I have served with honour and devotion, and especially – especially – I want to devote all my strength, all my time, and all my energy to proving my innocence.

The extremely serious allegations against him made the decision a foregone conclusion. Now, the race to succeed him begins.

Usually the position of head of the IMF has gone to a European, while the head of the World Bank has been an American. But with the rise of the Brics countries (Brazil, Russia, India and China) and the increasing power of emerging countries such as Mexico, Indonesia and South Africa, some have called for a non-westerner to be appointed head.

This looks unlikely to happen, however. The IMF is in the middle of dealing with the European sovereign debt crisis. For the next few years at least, its leader will be dealing with European problems and knocking the heads of European politicians and central bankers together. Below, Harry Key runs through a list of likely candidates for successor to DSK.

Runners and riders

Christine Lagarde

First woman to be finance minister in a G7 nation

After winning widespread support and praise for her policies responding to the financial crisis in France, she is seen by many economists as Europe's leading candidate for the post. She may be hurt by her French nationality, while her questionable links to the businessman Bernard Tapie will cause unease among those who want a scandal-free IMF chie.

Axel Weber

Former president of the German Central Bank

Weber is a leading candidate and is rumoured to be the favoured candidate of the German chancellor, Angela Merkel. However, some see his hawkish policy as too hardline for the IMF's current position on Europe's financial problems, particularly after the generous terms offered to European countries by the fund under Strauss-Kahn.

Kermal Dervis

Vice-president and director of the global economy and development programme, Brookings Institution

Dervis was credited with saving Turkey from bankruptcy in the early 2000s and was honoured by the Japanese government for his work as former head of the UN Development Programme. His solid contacts and personal relationships in Europe make him a strong candidate.

Gordon Brown

Former prime minister of the UK

Although James Wolfensohn, a former World Bank chairman, has claimed that there "is no one better" for the position, the absence of any support from the British government makes it unlikely that Brown will achieve his dream of leading the IMF.