The study of complex mixtures of interacting synthetic molecules has historically not received much attention from chemists, even though research into complexity is well established in the neighbouring fields. However, with the huge recent interest in systems biology and the availability of modern analytical techniques this situation is likely to change. In this tutorial review we discuss some of the incentives for developing systems chemistry and we highlight the pioneering work in which molecular networks are making a splash. A distinction is made between networks under thermodynamic and kinetic control. The former include dynamic combinatorial libraries while the latter involve pseudo-dynamic combinatorial libraries, oscillating reactions and networks of autocatalytic and replicating compounds. These studies provide fundamental insights into the organisational principles of molecular networks and how these give rise to emergent properties such as amplification and feedback loops, and may eventually shed light on the origin of life. The knowledge obtained from the study of molecular networks should ultimately enable us to engineer new systems with properties and functions unlike any conventional materials.