G protein-coupled receptors (GPCRs) are a large family of cell-surface proteins involved in the transduction of a wide range of signals to initiate appropriate cellular response. Chemokine receptors belong to this family and are important in mediating immunological responses such as chemotaxis. This thesis focuses on CXCR4 and ACKR3, which share CXCL12 as a common endogenous ligand. Both CXCR4 and ACKR3 have been reported to have increased expression levels in different forms of cancers, making the pharmacological modulation of the two receptors a popular avenue for drug discovery. The work carried out in this thesis aimed to address the following: understanding the mechanism of a CXCR4 antagonism, using ordinary differential equation models to describe CXCR4 signalling and pharmacology, and finally, studying the receptor crosstalk between ACKR3 and CXCR4. In the first study, we sought to understand the inverse agonism at CXCR4 by characterising a clinical candidate, Burixafor, or TG-0054. We showed that TG-0054 inhibited CXCL12 binding to the receptor, as well as Gαi and β-arrestin2 recruitment. We also observed that TG-0054 acted as an inverse agonist at the cAMP response, but unlike other inverse agonists, it did not monomerise CXCR4 dimers. We conclude that TG-0054 has a unique pharmacological profile and would be a valuable addition to the toolbox for studying CXCR4 pharmacology. In the second study, we used systems biology modelling to further analyse the kinetic data of CXCR4 signalling and inhibition with small molecules, to derive parameters related to the unique pharmacological profile of TG-0054. We constructed an ordinary differential equation-based mathematical model describing key steps in CXCR4 activation and signal transduction. We showed that, TG-0054 was predicted to have a slow dissociation rate from the CXCR4, and negatively affected receptor internalisation. We propose that these characteristics of TG-0054 contribute to its inverse agonism. In the third study, we examined the effect of ACKR3 co-expression on CXCR4 internalisation. ACKR3 has been proposed as a CXCL12 scavenger, by which it could limit CXCL12 availability to CXCR4. Using real-time receptor internalisation assay as well as systems biology modelling, we showed that while ACKR3 acted predominantly as a scavenger at low CXCL12 concentration, its co-expression at high CXCL12 concentrations increased the kinetics of CXCR4 internalisation with a different mechanism. Therefore, ACKR3 likely has additional roles in this signalling axis beyond that of a CXCL12 scavenger. The research presented in this thesis shed some light to the pharmacology and crosstalk of the CXCL12-CXCR4-ACKR3 signalling axis. We also showcased the utility of systems biology modelling in extracting insights from kinetic data as well as testing hypotheses on signalling mechanisms. Our work here contributes to the overall molecular-level understanding of CXCR4 and ACKR3 functions, which could act as foundation for future drug discovery efforts