The chapter focuses on two-sample studies with binary responses, mostly on the case where each sample has an independent binomial response. We discuss three parameters of interest based on the functions of the two binomial parameters: the difference, ratio, or odds ratio of the two parameters. The difference and odds ratio have symmetry equivariance, but the ratio does not. The odds ratio is useful for case-control studies. We compare two versions of the two-sided Fisher’s exact test, and recommend the central one. We describe compatible confidence intervals with the Fisher’s exact test using any of the three parameters of interest. Unconditional exact tests generally have more power than conditional ones, such as Fisher’s exact test, but are computationally more complicated. We recommend a modified Boschloo unconditional exact test with associated confidence intervals to have good power. We discuss the Berger–Boos adjustment, and mid-p methods. We compare several methods with respect to confidence interval coverage. We end with a different study design used with COVID-19 vaccines, where the number of total events is fixed in advance.