Shadow banking is about the size of the regulated banking system. It includes investment banks, hedge funds, money market funds, and private equity funds. New regulations will require that banks hold more capital in reserve as a cushion against potential losses. Essentially, this means that they will not be able to use the high levels of leverage that they have used in the past to increase potential profits and losses. Investors willing to take higher risks in order to achieve higher rates of return may take their business to the shadow banking system that has been growing fast, particularly in Europe.
The shadow banking system played a large role during the financial crisis. Unless regulations are imposed on the shadow banks, they will grow relative to regulated banks and we can look forward to future financial crises. The failure of the world's largest hedge fund in the US almost triggered a crisis prior to the Great Recession. The Fed organized a group of investment banks to intervene and restore order to the markets. That may not be possible the next time that this happens.