It is well known that materials with strong concentration gradients, e.g. diffusion couples, may exhibit porosity, internal stresses or even macroscopic deformations caused by the Kirkendall effect. Even though the Kikendall effect has been studied for many years there are still some unsolved issues. In order to gain a deeper understanding of the fundamentals of the Kirkendall effect computer simulations are an important tool. In this work we use newly developed computational methods to study the Kirkendall effect in binary and multicomponent alloys, and compare the results with experimental data. Exemples will be shown how these methods in combination with thermodynamic and kinetic data assessed by the CALPHAD method can be used to quantitatively predict the Kirkendall shift and porosity in alloys.