Our nervous system, like most information processing systems, faces 4 fundamental physical constraints. It has to transmit information quickly (1. time) and reliably (2. noise) while keeping its energy consumption (3. energy) and size/weight (4. spatial scale) at a minimum, to support the behaviourally determined fitness of the organism. These constraints are likely to enforce trade-offs to be made in the evolution of the nervous system. Taking this view, I investigated myelinated and unmyelinated axons across systems and species. I developed user interfaces and simulation methods for the Modigliani stochastic simulation software, and made a number of findings highlighted in the following. Myelinated axons make up the majority of long-range connections in CNS and PNS. I derived size-dependent relationships for metabolic costs of action potentials in myelinated axons. The high density of sodium channels at Nodes of Ranvier set lower limits on myelinated axons' outer diameter (0.3 μm), which is 3-fold that for unmyelinated axons. In contrast, thin, unmyelinated axons make up most of the local (cortical) connectivity. Using a variety of axon models and detailed models of synaptic calcium dynamics and vesicle release, I showed that the waveform of action potentials undergoes random changes whilst traveling along thin unmyelinated axons. These fluctuations translate into synaptic response variability. The diameter of unmyelinated axons sets energetic limits to signalling, and I derived diameter-dependent relationships for the maximum rate of burst and sustained firing. The latter depends on the density of pumps and metabolic cost of action potentials, but is counter intuitively independent of axon diameter. My findings provide insights and scaling-relationships that relate the 4 fundamental design constraints for wiring brains. They allow us to quantitatively predict structure-function relationships, and form a basis for principled treatments of nerve disorders. My findings provide insights and scaling-relationships that relate the 4 fundamental design constraints for wiring brains. They allow us to quantitatively predict structure-function rela- tionships, and form a basis for principled treatments of nerve disorders.