Despite their growing use, there is limited literature on the design and analysis of stepped-wedge trials (SWTs). The design is characterised by some or all clusters experiencing the control condition follow by the intervention condition. This enables within-cluster comparisons, but confounds the intervention effect with secular trends. In this thesis, I aim to use statistical methodology to improve the design efficiency and identify robust methods of analysis. I provide a new formulation of a design effect for an SWT. From this, I identify that it is more efficient for a trial to begin after the first clusters switch to the intervention, and end before the final clusters switch to the intervention. SWTs are commonly analysed using a mixed-effect model with a random effect for cluster and fixed effects for periods and the intervention. Through a wideranging simulation study, I found that this “standard” model is sensitive to deviations from model assumptions and suggest adding a random effect for period. However, this alternative model still suffered from confidence interval under coverage in some scenarios. I introduce a novel method of analysis that excludes the within-cluster comparisons. Each period of the trial is analysed separately to give within-period intervention effect estimates. An inverse-variance weighted average provides an overall effect and permutation tests provide a p-value and confidence intervals. In a simulation study, I find that this novel method provides unbiased inference in a range of scenarios, but had lower power than the standard model when the standard model was correctly specified. I introduce a new Stata command I have developed to conduct this novel method in order to encourage wider use of this new methodology. These finding will lead to trialists using more efficient trial designs and more robust analysis methods.