Résumé : While algorithms have been present in finance since the 1960’s, a confluence of factors in mathematical modeling, IT infrastructure, sociological context and legal-regulatory framework led to a turn of the paradigm at the turn of the millennium. Modern algorithmic and high frequency trading became a mythical topic of discussion, a trading practice almost indistinguishable from magic: too fast to be seen, too complex to be understood, too dangerous to be left on its own. A beast financial regulators had to deal with.This thesis describes how the emergence and development of modern algorithmic and high frequency trading (HFT) led financial markets to become a large complex adaptive system before describing the many regulatory attempts in the US and in the EU to deal with the issues of interconnected algorithms in finance.The history and regulatory experience point out to certain regulatory principles which together constitute a new regulatory paradigm, the paradigm of algorithmic regulation in finance.