This dissertation is based on the study of biological systems and aqueous solutions at low temperatures. The focus of the dissertation is on the continued development of low temperature biological small angle X-ray scattering (SAXS), cryoSAXS. CryoSAXS is a new method for biological SAXS that involves cryocooling the sample to 100 K. At 100 K the sample is much more resistant to damage from X-rays, enabling use of volumes hundreds or thousands of times smaller than in conventional room temperature SAXS. This work was divided into three main pieces. First, we designed, microfabricated, and tested new small volume, fixed path length sample holder for use in cryoSAXS. Next, as a first step towards answering the question of how much the radiation tolerance of a sample increases upon cryocooling, we developed methods to quantify radiation damage to SAXS profiles and tested these using standard room temperature SAXS. Finally, we measured the radiation tolerance of cryocooled SAXS samples, and found that the cryocooling decreases the radiation sensitivity by three orders of magnitude. The last chapter of the dissertation describes ongoing work to develop time resolved cryoSAXS, and other outstanding questions in cryoSAXS. In addition to cryoSAXS, in a complementary research project we studied ice formation in aqueous solutions. In particular, we quantified the critical warming rate, the warming rate required to prevent ice formation upon warming a vitrified solution. This has particular relevance to biological cryopreservation, as ice formation can irreparably damage cryopreserved samples.