This thesis uses femtosecond laser spectroscopy in studying strong correlation in condensed matters that are pertinent to future technology: a wide bandgap perovskite and a quantum material, with the employment of ultrafast time-resolved spectroscopy in the regime ranging from near-infrared (NIR), visible, ultraviolet (UV), to X-ray, tailed to the target materials. The first subject studied is the high-mobility perovskite oxide, barium stannate, intrinsic and doped. Primary results revealed by ultrafast broadband UV spectroscopy comprise the carrier injection dynamics pertinent to optoelectronics and photovoltaic applications and the hot carrier cooling via electron-phonon coupling, together with the effect of polaronic defect states. The second subject studied is the strongly correlated spin-orbit Mott insulator honeycomb iridate. An advanced X-ray spectroscopy apparatus dedicated to investigating light-driven quantum materials is described with spectroscopic evidence of modulation of inter-site hopping parameters. Further incorporation of broadband NIR and VIS transient spectroscopy dissects the non-equilibrium inter-site dynamics associated with the photodoped quasiparticles, i.e., holons and doublons, in a 2D honeycomb lattice.