In this review we discuss the chaotic dynamics (both classical and qua
ntal aspects) of a simple atomic system, namely hydrogen atom interact
ing with time independent and time dependent external fields. These in
clude: i) static electric field, ii) static magnetic field, iii) combi
ned electric and magnetic fields, in parallel and perpendicular config
uration, iv) instantaneous and generalized van der Waals field, v) mas
s anisotropy and vi) linearly and circularly polarized microwave field
s.