Independent replication is one of the most powerful methods to verify published scientific studies. In computational science, it requires the reimplementation of the methods described in the original article by a different team of researchers. Replication is often performed by scientists who wish to gain a better understanding of a published method, but its results are rarely made public. ReScience C is a peer-reviewed journal dedicated to the publication of high-quality computational replications that provide added value to the scientific community. To this end, ReScience C requires replications to be reproducible and implemented using Open Source languages and libraries. In this article, we provide an overview of ReScience C’s goals and quality standards, outline the submission and reviewing processes, and summarize the experience of its first three years of operation, concluding with an outlook towards evolutions envisaged for the near future.