Complex chemical systems, such as living biological matter, are highly organized structures based on discrete molecules in constant dynamic interactions. These natural materials can evolve and adapt to their environment. By contrast, man-made materials exhibit simpler properties. In this Review, we highlight that most of the necessary elements for the development of more complex synthetic matter are available today. Using modern strategies, such as controlled radical polymerizations, supramolecular polymerizations or stepwise synthesis, polymers with precisely controlled molecular structures can be synthesized. Moreover, such tailored polymers can be folded or self-assembled into defined nanoscale morphologies. These self-organized macromolecular objects can be at thermal equilibrium or can be driven out of equilibrium. Recently, in the latter case, interesting dynamic materials have been developed. However, this is just a start, and more complex adaptive materials are anticipated.