Understanding phase behavior of highly confined water, ice, amorphous ice, and clathrate hydrates (or gas hydrates), not only enriches our view of phase transitions and structures of quasi-two-dimensional (Q2D) solids not seen in the bulk phases but also has important implications for diverse phenomena at the intersection between physical chemistry, cell biology, chemical engineering, and nanoscience. Relevant examples include, among others, boundary lubrication in nanofluidic and lab-on-a-chip devices, synthesis of antifreeze proteins for ice-growth inhibition, rapid cooling of biological suspensions or quenching emulsified water under high pressure, and storage of H2 and CO2 in gas hydrates. Classical molecular simulation (MD) is an indispensable tool to explore states and properties of highly confined water and ice. It also has the advantage of precisely monitoring the time and spatial domains in the sub-picosecond and sub-nanometer scales, which are difficult to control in laboratory experiments, and yet allows relatively long simulation at the 102 ns time scale that is impractical with ab initio molecular dynamics simulations.