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Most liquids form a single glass or amorphous solid state upon rapid cooling. However, there are a few substances, relevant to scientific and technological applications, that can exist in at least two different amorphous solid states, a property known as glass polymorphism. Examples include silicon, silica, and in particular, water. In the case of water, experiments show the existence of a low-density (LDA) and high-density (HDA) amorphous ice that are separated by a dramatic, first-order like phase transition. In the first part of this talk, I will present results from extensive out-of-equilibrium molecular dynamics simulations of glassy water where we study (i) pressure- and (ii) heating-induced transformations between LDA and HDA. Our results show that MD simulations of simple water models can indeed reproduce the phenomenology associated to the LDA-HDA transformations. For example, simulations reproduce the sharp, large density changes (>20%) that characterize the LDA-HDA transformations. Tracing the LDA-to-HDA and HDA-to-LDA transformation temperatures in the P-T plane allows us to construct a "phase diagram" which is also consistent with experiments. One of the open questions in glassy water is what the glass transitions of LDA and HDA [T_g,LDA(P) and T_g,HDA(P)] are and in particular, how they vary with pressure. We address these questions by heating LDA and HDA at different pressures. Our simulations predict that T_g,LDA(P) is anomalous, i.e., it decreases with increasing pressure, while Tg,HDA(P) increases with increasing pressure. Surprisingly, we find that the glass transitions of LDA and HDA are related to the LDA-HDA transformations. In the last part of this talk, I will discuss the implications of water glass polymorphism to the behavior of glassy aqueous solution. I will present recent results from computer simulations on glassy water-glycerol mixtures at different concentrations and relate them with experimental data.