Cellular Information Processing Networks (CIPNs) are chemical networks of interacting molecules occurring in living cells. Through complex molecular interactions, CIPNs are able to coordinate critical cellular activities in response to internal and external stimuli. We hypothesise that CIPNs may be abstractly regarded as subsets of collectively autocatalytic (i.e., organisationally closed) reaction networks. These closure properties would subsequently interact with the evolution and adaptation of CIPNs capable of distinct information processing abilities. This hypothesis is motivated by the fact that CIPNs may require a mechanism enabling the self-maintenance of core components of the network when subjected to internal and external perturbations and during cellular divisions. Indeed, partially replicated or defective CIPNs may lead to the malfunctioning and premature death of the cell. In this thesis, we evaluate different existing computational approaches to model and evolve chemical reaction networks in silico. Following this literature review, we propose an evolutionary simulation platform capable of evolving artificial CIPNs from a bottom-up perspective. This system is a novel agent-based Artificial Chemistry (AC) which employs a term rewriting system called the Molecular Classifier System (MCS.bl). The latter is derived from the Holland broadcast language formalism. Our first series of experiments focuses on the emergence and evolution of selfmaintaining molecular organisations in the MCS.bl. Such experiments naturally relate to similar studies conducted in ACs such as Tierra, Alchemy and α-universes. Our results demonstrate some counter-intuitive outcomes, not indicated in previous literature. We examine each of these “unexpected” evolutionary dynamics (including an elongation catastrophe phenomenon) which presented various degenerate evolutionary trajectories. To address these robustness and evolvability issues, we evaluate several model variants of the MCS.bl. This investigation illuminates the key properties required to allow the self-maintenance and stable evolution of closed reaction networks in ACs. We demonstrate how the elongation catastrophe phenomenon can be prevented using a multi-level selectional model of the MCS.bl (which acts both at the molecular and cellular level). Using this multi-level selectional MCS.bl which was implemented as a parallel system, we successfully evolve an artificial CIPN to perform a simple pre-specified information processing task. We also demonstrate how signalling crosstalk may enable the cooperation of distinct closed CIPNs when mixed together in the same reaction space. We finally present the evolution of closed crosstalking and multitasking CIPNs exhibiting a higher level of complexity.