The double-helical DNA biopolymer is particularly resistant to bending and twisting deformations. This property has important implications for DNA folding in vitro and for the packaging and function of DNA in living cells. Among the outstanding questions in the field of DNA biophysics are the underlying origin of DNA stiffness and the mechanisms by which DNA stiffness is overcome within cells. Exploring these questions requires experimental methods to quantitatively measure DNA bending and twisting stiffness both in vitro and in vivo. Here, we discuss two classical approaches: T4 DNA ligase-mediated DNA cyclization kinetics and lac repressor-mediated DNA looping in Escherichia coli. We review the theoretical basis for these techniques and how each can be applied to quantitate biophysical parameters that describe the DNA polymer. We then show how we have modified these methods and applied them to quantitate how apparent DNA physical properties are altered in vitro and in vivo by sequence-nonspecific architectural DNA-binding proteins such as the E. coli HU protein and eukaryotic HMGB proteins.