The present work is a report on recent progress made in our understand
ing of electron-atom collisions in a laser field. To some extent it is
a continuation of a previous review covering a somewhat larger subjec
t (Can. J. Phys. 63 (1985) 907). We shall discuss the present status o
f investigations in this field from the theoretical as well as experim
ental point of view but most of the report will be devoted to an analy
sis of the various approximation schemes used at present in this field
to describe the different aspects of laser-assisted electron-atom int
eractions. As the table of contents shows, most of the work done so fa
r is treating the atom as a spectator, described by a potential and on
ly very little has been achieved over the years to include the atomic
structure into consideration since the inclusion of these structure ef
fects poses considerable computational problems. Since, for example, m
ultiphoton ionization and its inverse process laser-assisted recombina
tion may be considered as one half of a scattering process, it is quit
e natural that some of the theoretical techniques described here are a
lso of interest for the treatment of other multiphoton processes not c
onsidered here since there are several other recent reviews available
on these topics. (C) 1998 Elsevier Science B.V. All rights reserved.