One and two-photon photoabsorption of atoms and ions is the primary focus of this study, with special emphasis on photoabsorption in a laser-produced strontium plasma. The dual laser plasma (DLP) technique has been employed to carry out these studies and adapted to include an optical parametric oscillator (OPO), tuneable in the visible wavelength range (410-700 nm), to permit two-photon and two-colour photoabsorption investigations. The OPO was tuned to one and two photon resonances in Sr0 and Sr+ and the XUV photoabsorption spectrum was studied for various laser intensities and detunings from resonance. Fluorescence measurements were also made to elucidate the underlying excitation dynamics in the atom/ion after laser irradiation. Absolute photoionization cross-section measurements of the Kr-isoelectronic sequence (Rb+, Sr2+) were made at the ASTRID storage ring at the University of Aarhus, Denmark. These results were complemented by measurements made with the DLP technique. Inner-shell excitation studies in Pb2+, Bi3+ and Sr+ were also undertaken with the DLP technique. Detailed atomic structure calculations using the Cowan suite of codes, based on Hartree-Fock configuration interaction methods, were performed to generate synthetic spectra for comparison with experimental results.