  Future lepton colliders will be precision machines whose physics program
includes close study of the Higgs sector and searches for new physics via
polarised beams. The luminosity requirements of such machines entail very
intense lepton bunches at the interaction point with associated strong
electromagnetic fields. These strong fields not only lead to obvious phenomena
such as beamstrahlung, but also potentially affect every particle physics
process via virtual exchange with the bunch fields. For precision studies,
strong field effects have to be understood to the sub-percent level. Strong
external field effects can be taken into account exactly via the Furry Picture
or, in certain limits, via the Quasi-classical Operator method . Significant
theoretical development is in progress and here we outline the current state of
play.
