Research in systems and synthetic biology in the past decade has resulted in important advances in understanding as well as engineering cellular systems through the underpinning molecular networks. Furthermore, there is an increasing blurring of boundaries between natural and engineered cellular systems. Dissecting information processing through these molecular networks is a central aspect of this. This brings up a number of systems challenges to be tackled. In this thesis, we focus on the dissection of two features of information processing molecular networks, modularity and spatial organisation. Modularity, a basic and cross-cutting theme in engineering is a key underlying theme for both systems and synthetic biology. It is a basis for both building complex circuits in synthetic biology using bottom up approaches, and for understanding the behaviour of complex molecular networks in terms of their constituent building blocks. Spatial organisation is a hallmark of cellular systems ranging from bacteria to eukaryotes and an ingredient actively exploited in evolution. It is also a vital tool in manipulating and engineering the behaviour of molecular networks through multiple, recently developed tools focussing on compartmentalisation. In the first part of this thesis, we develop a systems engineering framework to understand the behaviour of a module within a network, accounting for different aspects of the module and the ambient network. In spatial organisation, we focus on multiple themes (i) the analysis and evaluation of compartmental models as appropriate descriptions of compartmentalised reacting systems, (ii) developing systems engineering frameworks for engineering spatially organised genetic circuits, (iii) a theoretical and systems framework for elucidating the effect of spatial organisation in molecular networks. Taken together, these studies provide systems tools and approaches for dissecting and engineering vital aspects of the complexity of cellular information processing systems.