This talk will be about wave packet dynamics in super-critical potentials for spin-0 bosons and spin-1/2 fermions in both first quantized and second quantized frameworks. In the first quantized framework I will introduce a semi-analytical method based on multiple scattering expansions (MSE). The MSE solves the issue of negative tunneling times in barrier traversals of spin-0 bosons, an issue that has in the past been attributed to the limitations of the first quantized formalism, and accounts for charge creation and the Klein paradox at the potential discontinuities. The MSE describes as well the propagation of spin-1/2 fermions wave packets through supercritical potential barriers and it is convergent. For both cases, numerical simulations using the finite difference method and the split operator method confirm our findings. In the second quantized framework we approach Klein tunneling using space-time resolved solutions to relativistic quantum field equations. We see that the multiple scattering characterizes the propagation bosons and fermions  created spontaneously from a super-critical potential barrier resulting in exponentially increasing numbers of bosons and asymptotically vanishing creation rate of fermions.  When propagating a wave packet, we find that no particle actually tunnels through the barrier. The transmission is instead mediated by modulations in pair production at each edge of the barrier caused by the incoming particle (holes in the case of fermions and enhancements in the case of bosons). Those modulations are exactly equal to the densities calculated inside the barrier in the first quantized theory.