Self-organization represents a ubiquitous transition from disorder to order. It plays a critical role in forming crystalline materials and functional structures in biology. Functional structures are generally hybrid on a multiple scale in which nano-structures are often organized in a specific way such that they can perform functions. There are two typical functional structures: static equilibrium structures and dynamic non-equilibrium structures. In this review, recent advances in understanding and mimicking functional structures are summarized. Although great advances have been achieved, it is still a big challenge to realize dynamic non-equilibrium structures. In this case, we suggest that the controlling of self-organization in active systems may be a route toward interactive and adaptive structures.