In times of accelerating earth system transformations and their potentially disruptive societal consequences, imagining and governing the future is now a core challenge for sustainability research and practice. Much social science and sustainability science scholarship increasingly engages with the future. There is, however, a lack of scrutiny of how the future is envisioned in these literatures, and with what implications for governance in the present. This article analyses these two aspects, building on the concept of "anticipatory governance." We understand anticipatory governance to broadly mean governing in the present to adapt to or shape uncertain futures. We review perspectives within public policy, futures studies, social-ecological systems, environmental policy and governance, transition studies, science and technology studies, and responsible research and innovation literatures. All these literatures engage explicitly or implicitly with the notion of anticipatory governance, yet from distinct ontological and epistemological starting points. Through our review, we identify four approaches to anticipatory governance that differ with regard to (a) their conceptions of and engagement with the future; (b) their implications for actions to be taken in the present; and (c) the ultimate end to be realized through anticipatory governance. We then map onto these four approaches a diverse set of methods and tools of anticipation that each engages with. In concluding, we discuss how these four approaches provide a useful analytical lens through which to assess ongoing practices of anticipatory governance in the climate and sustainability realm.