Drawing on our experiences conducting replications we describe the lessons we learned about replication studies and formulate recommendations for researchers, policy makers, and funders about the role of replication in science and how it should be supported and funded. We first identify a variety of benefits of doing replication studies. Next, we argue that it is often necessary to improve aspects of the original study, even if that means deviating from the original protocol. Thirdly, we argue that replication studies highlight the importance of and need for more transparency of the research process, but also make clear how difficult that is. Fourthly, we underline that it is worth trying out replication in the humanities. We finish by formulating recommendations regarding reproduction and replication research, aimed specifically at funders, editors and publishers, and universities and other research institutes.