The Bretton Woods system is commonly understood to refer to the international monetary regime that prevailed from the end of World War II until the early 1970s. Taking its name from the site of the 1944 conference that created the International Monetary Fund (IMF) and World Bank (International Bank for Reconstruction and Development), the Bretton Woods system was history's first example of a fully negotiated monetary order intended to govern currency relations among sovereign states. In principle, the regime was designed to combine binding legal obligations with multilateral decision-making conducted through an international organization, the IMF, endowed with limited supranational authority. In practice the initial scheme, as well as its subsequent development and ultimate demise, were directly dependent on the preferences and policies of its most powerful member, the United States.
The World Bank and its sister organization, the International Monetary Fund, were created at Bretton Woods New Hampshire in 1944. Together they are referred to as the Bretton Woods Institutions or BWIs.

The IMF's original mandate sets forth three main objectives: 1. To promote international monetary cooperation; 2. To facilitate the expansion of international trade; 3. To promote exchange rate stability.
The IMF achieves these objectives by advising member countries on their economic policies and by providing conditional assistance to member countries experiencing balance of payments problems. As from the above, the Bretton Woods System designed 2 institutions. Gordon Wendell writes that the International Monetary Fund (IMF) is concerned with the world of the short run: foreign exchange rates, the balance of payments, monetary standards, foreign exchange reserves, the financing of trade and the problems involved in handling international financial crises. The World Bank which was initially referred to as the International Bank for Reconstruction and development (IBRD) is also concerned with international lending to finance growth and development and the improvement of welfare. A third organization that was to deal with international trade was established in 1995 as the World Trade Organization was not established by the Bretton Woods.
The International Monetary Fund despite its objectives has been objected by some writers because of its nature of conditions (conditionalities) that the fund generally attaches to he assistance it grants to countries in balance of payments difficulties.
The Bretton Woods institutions are part of the UN structure. They are in the category of Specialized Agencies reporting to the UN Economic and Social Council, which reviews their work. But unlike the most UN agencies, the fund and the Bank were established pursuant to special treaties signed by their member countries, quiet independently of the UN Charter.
Reference
Gordon, W.,(1996); The UN and the Bretton Woods institutions: new challenges for the twenty-first century, Journal of Economic Issues

In another article, who rules the World’s Financial Markets? , Richard O’brien indicates that, concerns were raised about the global financial system in 1971 when the collapse of the fixed exchange rates of the Bretton Woods system put currencies at the mercy of the markets. The Bretton Woods System though collapse 24 years ago, the intuitions that it created notably the IMF and the World Bank have refused to die with it. The Britton Woods commission had a desire to further the workings of the international monetary system rather than to find a new role for these institutions. Relying on the market to regulate itself has been a popular refrain in the past decade, the commission concludes that the market have not performed the job well that world economic growth has suffered as a result. Their recommendations for managing the international monetary system was first, governments should strengthen their macroeconomic policies and achieve greater economic convergence, and second they should establish a more formal system of coordination to avoid excessive exchange rate misalignments and volatility. Mervyn King says, The International financial institutions set up by the Bretton Woods over 50 years ago were designed to deal primary with problems of current account imbalances, but in recent years major financial crises have originated in the capital account. Mervyn went on to indicate that the key difference between the world of the Bretton Woods and the world today is the size and volatility of private capital flows. In those days and now it was recognized that no system could ensure the compatibility of domestic monetary autonomy, stable exchange rates and free capital mobility.
Reference

O’brien, R., (1995); Who rules the World’s financial markets, Harvard Business Review
Mervyn, K.,(2001); The international financial system: A new partnership. Bank of England (Quartey Bulletin)