We are in the early stages of a new “intergenerational turn” in political philosophy. This turn is largely motivated by the threat of global climate change, which makes vivid a serious governance gap surrounding concern for future generations. Unfortunately, there is a lack of fit between most proposed remedies and the nature of the underlying problem. Most notably, many seem to believe that only piecemeal, issue-specific, and predominantly national institutions are needed to fill the intergenerational governance gap. By contrast, I argue that we should adopt a genuinely global approach that treats intergenerational questions as foundational, and advocates for new permanent institutions with ongoing responsibilities to act on intergenerational threats. In this essay, I summarize my diagnosis of the underlying problem—that we face a basic standing threat that I call the “tyranny of the contemporary”—and sketch my proposal for a global constitutional convention aiming at institutions with standing authority and a broad remit. I then develop some of these ideas further through responses to fellow advocates for reform who nevertheless consider my proposals to go too far. In particular, I reject a counterproposal made by Anja Karnein, who argues that reforms should address only threats whose negative impacts would cross a high threshold. I argue that this would leave future generations vulnerable to what I call “squandering generations”. Among other things, these intergenerational squanderers violate appropriate relationships between past, present, and future generations. Yet, in my view, a central task of defensible intergenerational institutions is to protect the future against such abuse.