Water in confined geometries has obvious relevance in biology, geology, and other areas where the material properties are strongly dependent on the amount and behavior of water in these types of materials. Another reason to restrict the size of water domains by different types of geometrical confinements has been the possibility to study the structural and dynamical behavior of water in the deeply supercooled regime (e.g., 150-230 K at ambient pressure), where bulk water immediately crystallizes to ice. In this paper we give a short review of studies with this particular goal. However, from these studies it is also clear that the interpretations of the experimental data are far from evident. Therefore, we present three main interpretations to explain the experimental data, and we discuss their advantages and disadvantages. Unfortunately, none of the proposed scenarios is able to predict all the observations for supercooled and glassy bulk water, indicating that either the structural and dynamical alterations of confined water are too severe to make predictions for bulk water or the differences in how the studied water has been prepared (applied cooling rate, resulting density of the water, etc.) are too large for direct and quantitative comparisons.