Heavy impurity accumulation poses a problem for the operation of tokamaks featuring tungsten plasma facing components. Early termination of the plasma due to tungsten accumulation is often observed following long living 3D MHD perturbations. Such scenarios are often observed in present tokamaks like JET and ASDEX-U, and may be of concern for future machines like ITER and the European DEMO. Finding a way of designing high performance scenarios while preventing tungsten accumulation is therefore crucial. This thesis aims at understanding and modelling heavy impurity transport in tokamak plasmas in the presence of long living 3D MHD ideal perturbations. In the first part of the thesis, we develop the theoretical framework to treat the problem, building on stellarator theory for the main ions, while including the effect of strong toroidal rotation that is only present in tokamaks. The orderings of the background ion species and the heavy impurity species are developed in detail. The background ions are subsonic which allows for the calculation of their flows using the stellarator 1/Μ collisional regime, while the heavy impurities flow supersonically which requires the inclusion of centrifugal effects for the impurity description. An expression for the neoclassical heavy impurity flux is obtained which helps identify the contrasting physics involved. In the second part of the thesis, we present the development of the numerical tools used to model the problem according to the theoretical framework presented. The usage of the VMEC code to obtain suitable 3D MHD equilibria is explained. Also, the development of new codes for calculating the background ion and heat flux flow of the ions, and the impurity flow from such magnetic equilbria is described. The heavy impurities are followed in this background plasma using the VENUS-LEVIS code. This code describes the guiding-center movement of the heavy impurities, accounting for the centrifugal and Coriolis drifts, as well as for the correct effect of friction and thermal forces exerted by the background ions on the impurities through a newly implemented collision operator. Finally, the numerical tools developed in this thesis are used to model the impact of long living 1/1 internal kink modes on heavy impurity transport. Heavy impurity accumulation is observed to occur rapidly in the presence of a 1/1 internal kink mode, contrary to what is observed in axisymmetry, in which off-axis accumulation occurs due to the strong rotation. These cases agree well with a JET pulse where tungsten accumulates following rapid growth of a continuous 1/1 mode. In the weakly 3D phase of the pulse, off-axis accumulation of tungsten is observed, whilst in the strong 3D phase of the pulse, strong tungsten on-axis accumulation is observed. The theoretical developments allow us to break down all the relevant physics effects. It is seen that such on-axis accumulation is due to the synergetic effect of the 1/1 mode, the strong toroidal rotation and the NTV ambipolar electric field.