The interaction of light with atoms and molecules is universal and relevant to everyday life. With the advent of light sources such as femtosecond laser oscillators and free-electron lasers (FELs), intense and ultra-short light pulses with well-characterized properties are available, which allow to study the interaction of light and matter in extreme regimes. Applying a two-color pump-probe approach, involving two light pulses, matter can be prepared in a well-defined state by the first pulse and then probed by interacting with the second pulse. In this thesis, the non-linear interaction of light pulses with small atoms and molecules in the gas phase is investigated with special emphasis on photoionization. For this purpose a new high harmonic generation (HHG) source has been characterized, that can be used in two-color experiments to either prepare or probe atoms or molecules that undergo non-linear interaction with another intense light pulse. Furthermore the fragmentation of molecular hydrogen was investigated in light fields at 800 nm and 400 nm as a benchmark experiment for a new experimental set-up. Following this, the fragmentation of the greenhouse gas methane in these optical fields of 800 nm and 400 nm was studied at varying intensities regarding the kinetic energies of the fragment ions generated in the non-linear interaction. The aim of this study was to unravel the influence of ionizing methane primarily by tunneling ionization at 800 nm or by multi-photon ionization at 400 nm on the kinetic energy of the photofragments. Finally, in a two-color experiment, the circular dichroism in multi-photon ionization of an atomic prototype system, ionic helium, was investigated. Using the intense, circularly polarized extreme ultraviolet (XUV) pulses delivered by the FERMI FEL at the LDM endstation atomic helium was ionized and excited into an oriented state in the same XUV pulse. A subsequent near-infrared (NIR) pulse with the same or the opposite helicity as the XUV pulse then ionized the helium ion from the prepared state via multi-photon ionization. This follow-up experiment improves on a previous one by introducing a temporal delay between the XUV and NIR pulses to avoid a population imbalance in the prepared helium ions, and by covering a wider and more dense range of NIR intensities. The influence of the helicity and intensity of the NIR pulses on the circular dichroism of the multi-photon ionization, observed by multi-photon and above-threshold ionization features in the photoelectron spectrum, is then studied regarding the AC-Stark shift, the Freeman resonances, the photoelectron angular distribution and different NIR wavelengths. The experimental results are compared to results from TDSE (time-dependent Schrödinger equation) calculations, which were done by collaborators.