Difficulties in reproducing results from scientific studies have lately been referred to as ``reproducibility crisis". Scientific practice depends heavily on scientific training. What gets taught in the classroom is often practiced in labs, fields, and data analysis. The importance of reproducibility in the classroom has gained momentum in statistics education in recent years. In this manuscript, we review the existing literature on reproducibility education. We delve into the relationship between computing tools and reproducibility through visiting historical developments in this area. We share examples for teaching reproducibility and reproducible teaching while discussing the pedagogical opportunities created by these examples as well as challenges that the instructors should be aware of. We detail the use of teaching reproducibility and reproducible teaching practices in an introductory data science course. Lastly, we provide recommendations on reproducibility education for instructors, administrators, and other members of the scientific community.