The most overlooked analytical technique in polymer science is DSC - differential scanning calorimetry.
The technique is pretty simple. Two small "pans", 1 containing the sample, the other empty, are heated (or cooled) at a constant rate and the difference in the amount of energy going to the two pans is monitored. (Hence the term "differential" in the technique's name.)
The most common use for the instrument is to study melting/crystallization behavior of materials. Melting/crystallization temperatures can be determined (look at the location of the peak) as well as the associated heat of fusion/crystallization (the area under the peak). If you know the value for a "perfect" crystal, you can then determine the % of crystallization in your sample.
But even beyond that, you can determine the glass transition temperature (it will appear as an offset in the curve, not a peak), you can determine if an sample is entirely cured (look for a small exotherm as you increase the temperature), and you can also use it to learn about antioxidants in a polymer. (Bring the sample to a constant temperature under N2, then switch over to O2. The longer it takes for the oxidation exotherm to show itself, the more antioxidants are present - a technique known as OIT, oxidation initiation time.) The list of other analyses that people have created with this instrument can go on for pages. All this from just a few milligrams of sample.
So why do I say the technique is so overlooked? It is one of the workhorse instruments here at Aspen Research (you should see the panic when the instrument is temporarily down) and I think most industrial polymer scientists and engineers would agree. I say the technique is overlooked as I've yet to see it discussed in any university classes, or even given proper treatment in a textbook (Billmeyer has less than a page of text on it, and Skoog mentions limited polymer application in passing.) I never learned of the technique in the classroom either as an undergraduate or graduate student, the two interns I had these last few years have not been taught about it either, nor have any of the recent hires. Dynamic mechanical analysis (DMA), gel permeation chromatography (GPC) and the Mark-Houwink equation (capillary viscometry) all get proper coverage, but not this versatile thermal technique.
I'm sure that there are some schools somewhere that teach it, but based on my experience, they are the exception and not the rule. Why is that?