This article reviews and discusses the recent progresses of studies with the concept of “Computational plasma fluid mechanics”. Computational demonstrations show that the inhouse simulation codes such as PLASTIPC (PLasma All-Speed Turbulence with Implicit Pressure Code) have captured hydrodynamic instabilities and reproduced flow dynamics in thermal plasma – nonionized gas coexisting systems. A unique method has made it feasible to study collective growth of binary alloy nanoparticles by numerical analysis. SPH (Smoothed Particle Hydrodynamics) method with incompressibility modification has achieved complex behaviors of molten metal involving phase change, flow, heat transport, material mixing, and large deformation during arc welding. It is essential to study thermal plasma processes as comprehensive fluid systems in which hot plasma, cold nonionized gas, and materials coexist. The viewpoint and approaches of fluid mechanics as well as plasma physics are indispensable. Computational study will play a more important role in giving us new and deeper insights.