Should we regulate complex securities, subject them to an FDA-style approval process, or limit who can invest in them? To answer these questions, one first needs to establish why complexity matters, and what defines a complex security. Complexity is an important concept in financial markets with boundedly rational agents, but that finding a workable definition of complexity is difficult. For example, while CDOs are viewed by most as highly complex, equity shares of financial institutions, whose payoff structures are even more complicated, are often seen as less complex. We point out three different ways in which boundedly rational investors can deal with complexity: (i) by dividing up difficult problems into smaller sub-problems or by using separation results, (ii) by using models – simplified pictures of reality, (iii) through standardization and commoditization of securities. Importantly, simply increasing the quantity of information disclosed to investors does not resolve complexity, since in the presence of bounded rationality it leads to information overload..