In this article, recent progresses in modeling and forecasting of tephra transport phenomena are reviewed. First, we describe elementary processes of the Tephra Transport and Dispersion Models (TTDMs) especially from the Lagrangian point of view. The processes consist of advection, diffusion, gravitational fallout, dry deposition, wet scavenging, aggregation, resuspension and so on, which are taken into the operational models of Volcanic Ash Advisories and Volcanic Ash Fall Forecasts in the world. Second, we show examples of volcanic ash cloud and tephra fall forecasts on the basis of the case studies of the eruptions at Eyjafjallajökull in 2010 and Shinmoe-dake volcano in 2011, respectively. Finally, some representative numerical weather prediction models which drive the TTDMs and verifications of the TTDMs are also described. Other important parameters of eruption source which give initial condition of the TTDMs are briefly remarked as future works.