In critically ill patients, the pathophysiology of sepsis can affect the interactions between the antibiotic, the bacteria and the patient, leading to potential therapeutic failure and the development of antibiotic resistance. It is well acknowledged that research that optimises antibiotic exposure will assist improvement of outcomes in this patient group. Although beta-lactam antibiotics, such as piperacillin and meropenem, are commonly selected for empiric therapy of sepsis, dosing is unlikely to be optimal. In patients without renal dysfunction, data suggests that disease-induced alterations to pharmacokinetic parameters result in low trough concentrations for significant periods within a dosing interval. Administration of these time-dependent antibiotics by continuous infusion has been suggested to improve the pharmacokinetic-pharmacodynamic profile. Knowledge of concentrations in the extracellular fluid of human tissue, which is the target site of most pathogens, is particularly instructive. Extracellular fluid concentrations can be determined using techniques such as microdialysis. Therefore, the principal aims of this Thesis were to determine the plasma and subcutaneous tissue pharmacokinetics of piperacillin and meropenem administered by bolus dosing and continuous infusion in critically ill patients with sepsis; and to use Monte Carlo simulations to compare the ability of different dosing strategies to achieve pharmacodynamic endpoints. This Thesis also sought to compare the clinical outcomes of bolus dosing and continuous infusion of a beta-lactam antibiotic, ceftriaxone, in a prospective randomised controlled trial and to perform a meta-analysis on clinical outcomes from other similar published studies. Finally, this Thesis aimed to systematically review the published literature to determine any correlation between antibiotic dosing and the development of antibiotic resistance. The results of the pharmacokinetic studies, using piperacillin and meropenem, indicate that beta-lactam distribution into subcutaneous tissue, in critically ill patients with sepsis, is less than that observed in previous studies in healthy volunteers yet superior to studies in patients with septic shock. This supports the notion that the peripheral concentration of drugs may be inversely related to the level of sickness severity. Administration by continuous infusion was found to maintain statistically significantly higher trough beta-lactam concentrations in both plasma and subcutaneous tissue. Further analysis of the plasma data using population pharmacokinetic modeling and Monte Carlo simulations described significant pharmacodynamic advantages for administering meropenem or piperacillin by continuous infusion to organisms with high minimum inhibitory concentrations. Given the documented pharmacodynamic advantages for administering beta-lactams by continuous infusion, a prospective randomized controlled clinical trial was conducted using the beta-lactam antibiotic ceftriaxone. In 57 critically ill patients, we found equivalence between continuous infusion and bolus dosing in the intention-to-treat analysis. However, our a priori analysis criteria, requiring patients receive at least 4-days antibiotic treatment, found significant clinical and bacteriological advantages for administration by continuous infusion. To further investigate any clinical differences between bolus dosing and continuous infusion of beta-lactam antibiotics, we performed a meta-analysis of all published studies. Our analysis of the 13 published prospective randomized controlled trials (846 hospitalised patients) showed equivalence of continuous infusion and bolus dosing. Possible confounders observed within, and between the studies, make interpretation of these results challenging. However, two large retrospective cohorts not included in the meta-analysis, found definitive clinical and bacteriological advantages suggesting further research may be appropriate. The possible relationship between antibiotic dosing, or exposures, on the development of resistance was investigated using a structured review of the published literature. Our analysis of relevant papers found a wealth of data describing increasing levels of resistance with sub-optimal antibiotic dosing, particularly for fluoroquinolone antibiotics, but also for other classes including beta-lactams. These results demonstrate the importance of optimizing antibiotic dosing to decrease the development of antibiotic susceptibility from sub-optimal dosing, particularly for critically ill patients who are likely to have low drug concentrations. The results of this Thesis, suggest that a large, prospective, multi-centre randomised controlled trial in critically ill patients with sepsis, is required to definitively determine the clinical utility of administration of beta-lactam antibiotics by continuous infusion.