The study of magma-forming silicate liquids has long been a major topic in computational geochemistry/geophysics.  A wide range of properties of silicate liquids including structure and speciation, density, thermodynamics, diffusivity, viscosity, mixing, etc. can now be studied within the framework of density functional theory. In recent years, we have simulated many key liquids in CaO-MgO-Al₂O₃-SiO₂–H₂Osystem using the first principles molecular dynamics method. This talk will focus on the calculated melt structures and transport properties, and their visualization-based analysis. Our study suggests that the melt properties are strongly dependent on pressure and temperature. The local coordination (such as Si-O coordination) and degree of polymerization dramatically increase on compression. Self-diffusion and viscosity coefficients vary by several orders of magnitudes over relevant pressure-temperature ranges, even showing dynamical anomalies in some liquids. Compositional effects including those of water are found to be substantial as well. Interactive visualization of atomic position-time series allow us to associate the predicted complex dynamical behavior with the structural changes occurring on compression and to understand the microscopic origin of compositional effects. Finally, I will discuss some of important implications for magma dynamics.