Researchers have employed diverse instructional strategies to impart science communication (SciComm) skills, a cherished 21st-century skill into undergraduate students. We reviewed the pedagogical strategies used in developing SciComm skills in undergraduates. This review revealed that analyzing data and scientific literature, increasing exposure to multiple writing contexts, providing multiple opportunities to present findings orally, and providing feedback are used to teach SciComm skills. Many instructors who implement course-based undergraduate research experiences (CURE) report improved SciComm skills as one of the benefits of CUREs. To decipher points of intersection among CUREs and SciComm pedagogical strategies, we also reviewed the literature on pedagogical strategies used during the implementation of CUREs. It was evident that analyzing experimental data and existing literature, writing manuscripts, proposals, lab notebooks, and oral presentation of findings with constructive feedback are commonly used in the implementation SciComm and CUREs. We contend that the implementation of CUREs frequently overlooks easy opportunities to incorporate pedagogies specifically designed to enhance undergraduates' science communication skills, thereby leading to a notable underutilization of these critical competencies. Nevertheless, a guiding framework on how to infuse SciComm into CUREs does not exist. To harness the power of CUREs to develop SciComm skills, we propose the CURE-Comm Framework.