Recently, increasing attention has focused on making causal inference when interference is possible, i.e., when the potential outcomes of one individual may be affected by the treatment (or exposure) of other individuals. For example, in infectious diseases, whether one individual becomes infected may depend on whether another individual is vaccinated. In the presence of interference, treatment may have several types of effects. We consider inference about such effects when the population consists of groups of individuals where interference is possible within groups but not between groups. In the first part of this research, we assume a two stage randomization design where in the first stage groups are randomized to different treatment allocation strategies and in the second stage individuals are randomized to treatment or control conditional on the strategy assigned to their group in the first stage. For this design, the asymptotic distribution of estimators of the causal effects are derived when either the number of individuals per group or the number of groups grows large. A simulation study is presented showing that in various settings the corresponding asymptotic confidence intervals have good coverage in finite samples and are substantially narrower than exact confidence intervals. The methods are illustrated with two applications which consider the indirect effects of cholera vaccination and an intervention to encourage voting. In the second part of this research, we consider drawing inference about causal effects in the presence of interference when two stage randomization is not possible. Inverse probability weighted and doubly robust estimators are proposed for use in this setting. These estimators will be used to analyze data from an observational study on rotavirus vaccination in Nicaragua.