We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type that show intermittent behaviour between getting attached to some clusters and evolving independently. Secondly, two different ways of cluster formation can be identified, namely self-organized clusters which have mostly intra-cluster couplings and driven clusters which have mostly inter-cluster couplings.

Random matrix theory, initially proposed to understand the complex interactions in nuclear spectra, has demonstrated its success in diverse domains of science ranging from quantum chaos to galaxies. We demonstrate the applicability of random matrix theory for networks by providing a new dimension to complex systems research. We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate the importance of randomness in interactions for deducing crucial properties of the underlying system. This paper provides an overview of the importance of random matrix framework in complex systems research with biological systems as examples.