The rise of increasingly complex algorithms calls for critical thought about how best to prevent, deter, and compensate for the harms that they cause. This Article argues that the criminal law and tort regulatory systems will prove no match for the difficult regulatory puzzles algorithms pose. Algorithmic regulation will require federal uniformity, expert judgment, political independence, and pre-market review to prevent without stifling innovation the introduction of unacceptably dangerous algorithms into the market. This Article proposes that certain classes of new algorithms should not be permitted to be distributed or sold without approval from a government agency designed along the lines of the FDA. This "FDA for Algorithms" would approve certain complex and dangerous algorithms when it could be shown that they would be safe and effective for their intended use and that satisfactory measures would be taken to prevent their harmful misuse. Lastly, this Article proposes that the agency should serve as a centralized expert regulator that develops guidance, standards, and expertise in partnership with industry to strike a balance between innovation and safety.