Organisms are subject to the laws of physics, so the process of evolution is constrained by these fundamental laws. Classic and recent studies of the biophysical limits facing organisms have shown how fundamental physical constraints can be used to predict broad-scale relationships between body size and organismal biomechanics and physiology. In this talk I will provide a broad framework for the connection between physical constraints, evolution, and allometric physiology. I will focus on an under-appreciated aspect of allometry: ultimate limits that occur at distinct scales for broad categories of organisms. I will connect these limits to higher-order evolutionary phenomena such as major evolutionary transitions and constraints on populations of organisms. In discussing these concepts I will cover case-studies ranging from bacterial physiology to mammalian population dynamics.