Representing distributions in a metrics-based monitoring system is both important and hard. Doing it right unlocks many powerful use cases. What does Prometheus offer in this regard? And what are the pitfalls with the current state of the art? To help understand the present, this talk will also shed light on the past. How have the Histogram and Summary metric types become what they are today with all their weal and woe? Finally, let's have a look at the rich body of research happening in the area, and how it might benefit future versions of Prometheus.