We are starting publication of a series of featured articles entitled “Multiphase Computational Fluid Dynamics for Industrial Processes.” In this short Introduction we can only touch upon some of the important issues of industrial computational fluid dynamics (CFD) applications. It is difficult to underestimate the importance of CFD for modern industries. Advanced technologies require powerful computational tools to avoid expensive large-scale experiments and speed-up process and equipment optimisation. CFD is a rapidly evolving discipline oriented on developing computational tools for solving problems related to transport processes: fluid mechanics, heat and mass transfer, reactive flow, multiphase flow. In narrow terms CFD is the numerical solution of the mass, momentum, and energy conservation equations with properly defined boundary conditions. Those equations may be supplemented with (Newtonian or non-Newtonian) constitutive equations and equations of state for compressible fluids. In broader terms CFD also involves modelling (parameterisation) of phenomena at length and time scales that are too small to be fully resolved computationally; the three most prominent examples being turbulence, flows involving multiple phases, and reactive flows. In strongly turbulent flows, the spectrum of length and time scales is simply too wide to be completely resolved in a single computation. Models for small-scale turbulence are used to alleviate the computational burden and make simulations of large-scale industrial turbulent flows possible. Multiphase flows usually take the form of a continuous phase that carries one or more dispersed phases. The solid particles, or droplets, or gas bubbles that constitute the dispersed phases are often too small to be fully resolved; their impact on the macroscopic flow patterns needs to be modelled. A similar multi-scale issue relates to chemically reacting flow where mixing at the micro (molecular)-scale defines the rate of chemical reactions. The most important issue in predictive modelling of chemical industrial processes is how to deal with their multiphase character. Process equipment (chemical reactors, burners, mixers, crystallizers, hydro and pneumatic conveying pipe lines, fluidized beds, flotation cells) usually operates with multiple phases, modelling of which is much more complicated than that of a single phase flow. In dependence on the phases composing the flow system, the geometry of the flow domain and the process conditions (flow rates, agitation speeds), an abundance of flow regimes and flow phenomena can be distinguished. Resolving and predicting these in a numerical simulation is a clear and grand challenge. Key in virtually any simulation effort is to distinguish between the relevant and irrelevant physics and model what is relevant. Though, general mathematical descriptions of multiphase processes are known, it is practically impossible to solve all the conservation equations numerically without simplifications. There are the two major groups of approaches, which are currently used in engineering and science