The ability to probe and manipulate electron dynamics and correlations on their characteristic time scales would open up many technological\nand scientific possibilities.\nWhile modern laser technology already allows to\ndo that in principle, a lot of theoretical ground work is still missing.\nThis thesis focuses on the elementary effect of laser strong field ionization of the two\nsimplest systems: The Hydrogen and Helium atoms.\nTo that end, the time-dependent Schroedinger equation is solved numerically, and photo-electron spectra are extracted\nusing the highly efficient tSurff technique.\n\nWe implemented both the one and two particle versions of tSurff together with several other numerical techniques in a new\nparallelizable C++ code. We provide details \non the employed methods and algorithms, \nand study numerical efficiency properties of\nvarious approaches.\nWe propose a description of the electric field interaction\nin a mixture of length and velocity gauge\nfor the correct and most efficient \nimplementation of a coupled channels approach,\nwhich can be used\nto compute accurate single ionization photo-electron spectra\nfrom true multi-electron systems,\neven molecules.\n\nWe provide extensive numerical data for a detailed study\nof the Hydrogen atom in an Attoclock experimental setup,\nwhere it is found that \nthe involved strong field tunnel ionization processes\ncan be considered instantaneous.\nIn particular, there appear no tunneling delays, which\ncan be used as a calibration for experiments with \nmore complicated targets.\n\nSimilarly, it is investigated whether discrepancies \nbetween theory and experimental\ndata for the longitudinal photo-electron momentum spread, resulting\nfrom photo-ionization of Helium in \nelliptically polarized laser pulses,\ncan be explained by non-adiabatic effects,\nand a related consistency problem \nin current laser intensity calibration\nmethods is pointed out.\n\nWe further show that Fano resonance line shapes\nof doubly excited states in the Helium atom,\nprominently appearing in single ionization spectra \ngenerated by short wavelength laser pulses,\ncan be controlled by an external long wavelength streaking field.\nThe resulting line shapes are still characterized\nby the general Fano situation, but with\na complex - rather than real - Fano parameter.\nWe provide a theoretical description of this two color process\nand prove numerically that the entire doubly excited state series\nexhibits synchronized \nline shape modifications as the specifics of the\ninvolved states are unimportant.\n\nFinally, we compute fully differential double ionization spectra\nand suggest a measure of correlation that is directly applicable\nto experimental data.\nWe confirm literature results at short wavelengths,\nand achieve to compute five-fold differential\ndouble ionization photo-electron\nspectra at infrared wavelengths from the Helium atom,\nthereby reproducing a characteristic\nseveral orders of magnitude\nenhancement of double emission due to \ncorrelation effects.