Interactive computer simulations are commonly used as pedagogical tools to support students' statistical reasoning. This paper examines whether and how these simulations enable their intended effects. We begin by contrasting two theoretical frameworks—dual processes and grounded cognition—in the context of people's conceptions about statistical sampling, setting the stage for the potential benefits of simulations in learning such conceptions. Then, we continue with reviewing the educational literature on statistical sampling simulations. Our review tentatively suggests benefits of the simulations for building statistical habits of mind. However, challenges seem to persist when more specific concepts and skills are investigated. With and without simulations, students have difficulty forming an aggregate view of data, interpreting sampling distributions, showing a process-based understanding of the law of large numbers, making statistical inferences, and context-independent reasoning. We propose that grounded cognition offers a framework for understanding these findings, highlighting the bidirectional relationship between perception and conception, perceptual design features, and guided perceptual routines for supporting students' meaning making from simulations. Finally, we propose testable instructional strategies for using simulations in statistics education. Significance: Interactive computer simulations are popularly used to teach statistical sampling and inference. A substantial body of classroom-based design research has emerged over the last two decades on this topic, paralleling the interest of cognitive psychologists in statistical reasoning. This review bridges the gap by synthesizing diverse literature, from laboratory-based cognitive research to classroom-based design research, to investigate people's reasoning about statistical sampling with interactive computer simulations. We organize the commonly occurring findings from these studies under a grounded cognition framework. Using this framework, we also identify instructional design strategies that future empirical researchers can test and statistics and data science practitioners can adopt. First, we highlight the importance of repeated exposure to simulations in a way that fosters creating perception–action routines aligned with mathematical principles. Second, we argue that intuitive representations ground students' meaning making from simulations, and idealized representations help generalize learning. Third, we recommend that visual routines be guided during activities with simulations. Fourth, we note the separate affordances of simulations and verbal materials. Lastly, we propose that statistical processes depicted in the simulations should be reified as foundations for more advanced concepts and practices. Overall, the paper contributes to the learning theories and instructional design in the context of simulation-based learning in statistics. [ABSTRACT FROM AUTHOR]