Runaway electrons (RE) generated during disruption represent a serious threat for the future Tokamaks. In fact, RE can cause unrecoverable damages to the plasma facing components once they reach the plasma edge. In order to mitigate the RE, it is vital to understand their interactions with the core plasma where the characteristics of RE current are defined. The goal of this work is to present an approach to studying the dynamics of RE from the core to the edge. On one hand, the mutual interaction of the RE with the magnetic reconnection instability in a weakly collisional plasma is analyzed. The results of this analysis will then be used to study the damage that the RE current can cause to the first wall of the reactors. Here, we present the first results of such an approach both for the core region and the edge. Concerning the physics of the core, we want to address the problem of the tearing stability of a post-disruption weakly collisional plasma where the current is completely carried by runaway electrons. The final goal is to extend the work in Helander et al. (2007) and Liu et al. (2020), where a resistive plasma was considered, to regimes where the magnetic reconnection can be driven also by the electron inertia. Specifically, it has been demonstrated in Helander et al. (2007) that the presence of RE in plasma has a significant effect on the saturated magnetic island width. In particular, RE generated during disruption can cause an increase of 50% in the saturated magnetic island width with respect to the case with no REs. This is detrimental for the reactor since MHD instabilities can break the confinement of the plasma leading to huge thermal loads on the first wall or generate further instabilities in the plasma. These results were obtained adopting a periodic equilibrium magnetic field that limited the analysis to small size saturated magnetic islands. Here we present our first results to overcome this limitation adopting a non-periodic Harris' type equilibrium magnetic field. The analysis of the interaction of RE with the first wall materials was carried out using the Monte Carlo-based code FLUKA. In particular, the volumetric energy deposition curves were obtained in tungsten and carbon tiles hit by runaway electrons with a Gaussian energy distribution curve in the range of MeVs. In addition, a parametric study was done to assess the dependence of the energy deposition curves on input parameters such as the impact angle. As was expected, the tungsten tile experienced an energy deposition concentrated in a smaller volume with respect to carbon due to a higher electronic stopping and elastic scattering. In fact, the tungsten density is around 10 times higher than the carbon density and its charge is around 12 times than the carbon charge. These differences also influenced the near-surface behavior of the electrons at different impact angles in the two materials with carbon being more sensitive to a change in impact angle with respect to tungsten. Helander, P., Grasso, D., Hastie, R. J., & Perona, A. (2007). Resistive stability of a plasma with runaway electrons. Physics of Plasmas, 14(12), 122102. Liu, C., Zhao, C., Jardin, S. C., Bhattacharjee, A., Brennan, D. P., & Ferraro, N. M. (2020). Structure and overstability of resistive modes with runaway electrons. Physics of Plasmas, 27(9), 092507.