  In strong electromagnetic fields, new plasma phenomena and applications
emerge, whose modeling requires analytical theories and numerical schemes that
I will develop in this thesis. Based on my new results of the classical plasma
model, the role of strong magnetic fields during laser-plasma interactions can
now be understood. Moreover, based my new quantum electrodynamics (QED) models
for plasmas, it is now possible to understand strong-field QED effects in
astrophysical environments and test them in laboratory settings.
