This paper reviews recent research on causal inference with large-scale assessments in education from a Bayesian perspective. I begin by adopting the potential outcomes model of Rubin ("J Educ Psychol" 66:688-701, 1974) as a framework for causal inference that I argue is appropriate with large-scale educational assessments. I then discuss the elements of Bayesian inference arguing that methods and models of causal inference can benefit from the Bayesian approach to quantifying uncertainty. Next I outline one method of causal inference that I believe is fruitful for addressing causal questions with large-scale educational assessments within the potential outcomes framework--namely, propensity score analysis. I then discuss the quantification of uncertainty in propensity score analysis through a Bayesian approach. Next, I discuss a series of necessary conditions for addressing causal questions with large-scale educational assessments. The paper closes with a discussion of the implications for the design of large-scale educational assessments when the goal is in asking causal questions and warranting causal claims.