Cultivating in preservice science teachers (PSTs) the competence required to teach scientific models and modeling is a valued outcome of teacher preparation programs. However, science teacher educators face inherent tensions when designing and implementing teacher preparation experiences to achieve this outcome. In this systematic review, we first propose five sets of design tensions that science teacher educators need to navigate. We identify empirical intervention studies that aimed to develop PSTs' professional competence for teaching scientific models and modeling and analyze how the reviewed interventions addressed the design tensions, and examine their outcomes. Our analysis reveals that the reviewed interventions prioritized the development of PSTs' cognitive aspects of teacher professional competence for teaching scientific models and modeling while giving limited attention to affective-motivational aspects and the need to simultaneously develop aspects of PSTs' competence not specific to scientific models and modeling. The interventions were more successful in enhancing PSTs' declarative knowledge than enacted knowledge and affective-motivational aspects. However, the nature of modeling activities included in the interventions varied widely, posing challenges in identifying critical features that led to the identified positive outcomes. The interventions reported mixed outcomes in developing PSTs' enacted knowledge in teaching contexts, even when incorporating activities for knowledge application and knowledge transfer beyond the intervention context. We discuss the implications of these findings and provide recommendations for better-preparing PSTs to teach scientific models and modeling. We also discuss the unique affordance of using the design tension framework to analyze the interventions.