Rheological measurements offer a unique means of interrogating the physics of amorphous solids, including crosslinked rubbers and polymeric glasses. Here, we present several vignettes to demonstrate the ability of both classical and novel rheological experiments to resolve important questions in condensed matter physics. First, results from torque and normal force measurements aimed at understanding the thermodynamics and mechanics of polymer networks in both dry and swollen states are presented. In particular, we examine the validity of the Frenkel-Flory-Rehner theory of rubber network swelling. Torsion and normal force measurements are also described for a series of polymeric glasses that exhibit similar shear moduli but, surprisingly, very different normal force responses, with one set of materials showing extreme deviations from neo-Hookean behavior and the other being close to neo-Hookean. We then describe the use of a novel torsional dilatometer, which allows simultaneous measurement of mechanical properties and volume recovery, to investigate the aging and rejuvenation behaviors of glassy polymers. Also, the temperature dependence of dynamics is probed in glassy polymers that have been aged into equilibrium below the nominal glass transition temperature and evidence is presented that time-scale divergence may not be a true signature of the glass transition itself. Finally, we describe a reduction in scale of the classical membrane inflation test to allow measurement of the biaxial creep compliance of nanometer thick polymeric films using an atomic force microscope. In each instance, emphasis is placed on how the measurements are designed to interrogate the physics of interest in the materials investigatedx.