This report summarizes the presentations and discussion sessions at the Dagstuhl Seminar 21302 "Approximate Systems" that took place during July 25 - 30, 2021. Due to COVID, the seminar was held in a hybrid fashion, with around 1/3 of the attendees on-site and the remaining ones online. The seminar discussed advances and open challenges in applying approximate computing techniques across the stack and across different application domains, and we hope that this report can provide a useful resource also for other researchers.