The fields of protein crystallography, cryo-electron microscopy and cryopreservation require that aqueous biological samples or aqueous solutions be cooled to very low temperatures. The outcomes of experiments in those fields also depend on the behavior of the water contained in such samples. This makes understanding that behavior central to such experiments, even if that understanding is not the aim of the research. In particular, samples often must be cooled so that the water is in a metastable amorphous state, i.e. so that no crystalline ice forms. This dissertation covers topics ranging from the very practical matter of how this metastable state can be achieved and maintained to more fundamental questions surrounding its formation. A cheap and simple method by which tiny samples can be cooled at very high rates is demonstrated, which will allow cooling at rates previously requiring expensive and complicated apparatus. The relationship between the cooling rate required to produce an amorphous sample and the amount of solute in the sample is demonstrated to be a simple exponential, which may indicate the fundamental mechanism by which ice forms from supercooled solution. Finally, the radiation sensitivity of protein crystals is shown to be linked with the diffusive motions of the supercooled solvent within them: radiation sensitivity is suppressed by lowering the temperature because diffusive motion is also suppressed.