Abstract: There are a number of "fundamental bounds” in physics. For instance, special relativity dictates nothing can travel faster than the speed of light; Heisenberg’s uncertainty principle limits the accuracy with which position and momentum can be simultaneously measured. In addition to fundamental bounds, there are also approximate or “heuristic” bounds which, despite being approximate, can nevertheless be remarkably useful. This is especially true in more complex systems, where the notion of a bound can provide a unifying framework by which to understand apparent universal phenomena observed across different systems. I will present theoretical work on two such heuristic bounds in solid-state systems: The first is an approximate upper bound on the superconducting transition temperature and the second is a related bound on the scattering rate in normal conductors. The former bound has implications in the ongoing search for higher temperature superconductors while the latter sheds light on so-called “Planckian” transport observed in otherwise conventional metals.