Peer review is an important part of the scientific process, but traditional peer review at journals is coming under increased scrutiny for its inefficiency and lack of transparency. As preprints become more widely used and accepted, they raise the possibility of rethinking the peer-review process. Preprints are enabling new forms of peer review that have the potential to be more thorough, inclusive, and collegial than traditional journal peer review, and to thus fundamentally shift the culture of peer review toward constructive collaboration. In this Consensus View, we make a call to action to stakeholders in the community to accelerate the growing momentum of preprint sharing and provide recommendations to empower researchers to provide open and constructive peer review for preprints.