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Two-component systems (TCSs) are critical for bacteria to interact with their extracellular environment. They define a type of signalling system that is composed of a transmembrane histidine kinase (HK) and a cytoplasmic response regulator (RR). In this thesis we have studied the evolutionary and functional aspects of these important signalling systems. By studying the distribution of the TCS orthologues of E.coli across more than 900 bacterial organisms, we have found that a pair of TCS proteins does not always coexist in one organism. The genomic localisation map of TCSs reveals a possible translocation mechanism for TCS evolution. The alignments of HKs and RRs have shown that HKs are genetically more divergent, probably due to their signal recognizing role. An analysis of the steady states of TCS dynamics has shown that the outputs of the TCSs are bistable if they have positive auto-regulation feedback loops in their transcriptional regulation. Our analysis has also shown that the phosphorylation process of a TCS is always monostable and the factors that affect steady states have been studied. For both orthodox and non-orthodox TCSs, autophosphorylation rates of the HKs are the most important factor to affect the steady states of the TCSs' outputs. To study the phosphorelay mechanism of the non-orthodox TCS ArcB/A, we constructed plasmids carrying different copy numbers of ArcB mutants with different phosphorylation sites ablated. By fitting our phosphorelay model to the data obtained from mutant ArcB constructs, we have found that ArcB most likely performs phosphorelay in an allosteric mechanism. Finally, Approximate Bayesian computation was used in order to evaluate the potential use of orthodox TCS and non-orthodox TCS architectures in synthetic biology contexts. Results show that neither of the orthodox TCS model or the nonorthodox TCS model are superior under all circumstances but that both models have advantages in some scenarios. In the appendix, we did some study on how the contact residue disorder would affect protein-ligand binding specificity.