The field of supramolecular chemistry focuses on the non-covalent interactions between molecules that give rise to molecular recognition and self-assembly processes. Since most non-covalent interactions are relatively weak and form and break without significant activation barriers, many supramolecular systems are under thermodynamic control. Hence, traditionally, supramolecular chemistry has focused predominantly on systems at equilibrium. However, more recently, self-assembly processes that are governed by kinetics, where the outcome of the assembly process is dictated by the assembly pathway rather than the free energy of the final assembled state, are becoming topical. Within the kinetic regime it is possible to distinguish between systems that reside in a kinetic trap and systems that are far from equilibrium and require a continuous supply of energy to maintain a stationary state. In particular, the latter systems have vast functional potential, as they allow, in principle, for more elaborate structural and functional diversity of self-assembled systems - indeed, life is a prime example of a far-from-equilibrium system. In this Review, we compare the different thermodynamic regimes using some selected examples and discuss some of the challenges that need to be addressed when developing new functional supramolecular systems.