Across research disciplines, cluster randomized trials (CRTs) are commonly implemented to evaluate interventions delivered to groups of participants, such as communities and clinics. Despite advances in the design and analysis of CRTs, several challenges remain. First, there are many possible ways to specify the causal effect of interest (eg, at the individual‐level or at the cluster‐level). Second, the theoretical and practical performance of common methods for CRT analysis remain poorly understood. Here, we present a general framework to formally define an array of causal effects in terms of summary measures of counterfactual outcomes. Next, we provide a comprehensive overview of CRT estimators, including thet‐test, generalized estimating equations (GEE), augmented‐GEE, and targeted maximum likelihood estimation (TMLE). Using finite sample simulations, we illustrate the practical performance of these estimators for different causal effects and when, as commonly occurs, there are limited numbers of clusters of different sizes. Finally, our application to data from the Preterm Birth Initiative (PTBi) study demonstrates the real‐world impact of varying cluster sizes and targeting effects at the cluster‐level or at the individual‐level. Specifically, the relative effect of the PTBi intervention was 0.81 at the cluster‐level, corresponding to a 19% reduction in outcome incidence, and was 0.66 at the individual‐level, corresponding to a 34% reduction in outcome risk. Given its flexibility to estimate a variety of user‐specified effects and ability to adaptively adjust for covariates for precision gains while maintaining Type‐I error control, we conclude TMLE is a promising tool for CRT analysis.