Abstract: The light isotope of Helium - 3He - is the purest phase of matter in nature. Zero-point fluctuations drive any impurity out of the bulk liquid. However, helium can be impregnated into porous glass. Silica aerogel is a solid formed from a network of strands and clusters of SiO2 that is almost entirely empty space. The system of quantum liquid infused into silica aerogel provides an novel system for studying the effects of disorder on the relative stability of ordered phases near a quantum critical point. I will describe some of the key experiments, and related theoretical interpretations, that have been carried which elucidate the role of disorder on the properties of both normal and superfluid 3He. These studies may also provide deeper insight into porous media with complex structure. The gossamer structure of silica aerogel is a realization of a random fractal - a solid with no long-range order, but power-law scaling of the density correlation function. I will also discuss possibilities for observing the effects of fractal correlations in the disordered medium on the properties of liquid 3He.