The dollar’s continuing role as the world’s key currency has come into doubt. What might replace the dollar if it collapses or becomes unmanageable? Let’s hope it doesn’t, but we should be ready with ideas just in case. Even if our current system survives, contemplating radical alternatives can provide a new perspective on it and on possible improvements. Just as conjectural or “what-if?” history can improve our understanding of the actual course of events, so “whatif?” monetary systems may help us better understand, by contrast, what we now have. How would a system function without a dominant issuer whose banknotes and deposits defined the unit of account?