Various aspects of Water Dynamics are discussed; (1) Fluctuation and relaxation in hydrogen bond network rearrangement and their observation, (2) Mechanism of water freezing, and (3) Proton transfer in liquid water and ice. Liquid water yields the intermittently collective motions accompanied with large fluctuations. Various relaxation processes associated with these collective motions in liquid water yield so-called 1/f spectra. We present the result of our analysis on a method, called 2-dimensional Raman/IR spectroscopy. This method will be able to deal with the mechanism of these intermittent collective motions. Upon cooling, water freezes into ice. This process is a most familiar phase-transition, occurring in many places in nature, but has never been successfully simulated by a computer simulation. We report the first successful simulation for the pure water freezing process, which gives a molecular level picture of, particularly, how an initial nucleus is created and grows. The proton transfer is a most basic reaction in chemistry and biochemistry. It is found that the mechanism of the proton transport in ice is completely different from that in liquid water. The repulsion from fourth coordinated water makes the facile proton transfer possible. The long range solvation is essential for the smooth transport of the proton in ice.