To most people, especially theorists, measuring the electrical resistivity of a metal sounds like an almost trivial measurement! Surely, you just stick a sample of the metal between the leads of an ohm-meter and read off the resistance!
The temperature dependence of the resistance can provide significant information about scattering of quasi-particles in the metal and any decent theory should be able to describe it. A famous case it the "linear in T" resistivity of optimally doped cuprate superconductors, a signature of non- Fermi liquid behaviour.
Most of the interesting strongly correlated metals (cuprates, organic charge transfer salts, iron pnictides, ....) have layered crystal structures leading to anisotropic electronic properties. These are sometimes referred to as quasi-two-dimensional metals.
Accurately, measuring the resistivity (and its temperature dependence) in the three different directions though is a highly non-trivial exercise. Basically, this is because you have to be sure that the current is going through the sample in the direction you think it is.
This is highlighted in a recent Nature Communications article from Nigel Hussey's group. They state:
In a quasi-1D conductor, it is especially problematic to measure the smallest of the resistivity tensor components, because even a small admixture of either of the two larger orthogonal components can give rise to erroneous values and distort the intrinsic temperature dependence of the in-chain resistivity. In Li0.9Mo6O17, reported room-temperature values for the in-chain (b axis) resistivity range from 400 μΩ cm23 to more than 10 mΩ cm34, 35.Reported values for the ratio of the a to b axis resistivity vary from about 2 to 100!
This is a very large discrepancy!
I wrote this post because I thought I had come up with a fancy theoretical explanation of why in one paper the resistivity anisotropy ratio was only ~4, whereas band structure predicts a much larger value. However, when I surveyed the literature I discovered the result I was so proud of explaining is probably an artefact!