Probing and controlling the flow of charge and dynamics within a molecule following photoexcitation is a fundamental requirement for the targeted synthesis of the next generation of molecules and materials designed for artificial light-harvesting, photochemical energy conversion, and photocatalysis. X-rays, by virtue of their temporal resolution, atomic-specificity, and chemical environment sensitivity, are ideal probes to study ultrafast processes including electron and proton transfers and couplings in molecules in non-equilibrium conditions. Emerging X-ray free electron laser (XFEL) sources offer novel probes of chemical systems, in the gas and condensed phases, with unprecedented spatial and temporal resolutions. Extracting microscopic details from these state-of-the-art experiments hinges on our ability to simulate the underlying electronic and structural dynamics and our ability to interpret and predict X-ray spectroscopic observables. This is essential for the design of sophisticated multi-pulse experiments and for their interpretation. Over the last two decades, both real-time (RT) and linear-response (LR) time-dependent density functional theory (TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this talk, some of our theoretical efforts, based on the TDDFT framework, covering static and transient X-ray absorption and emission, resonant inelastic X-ray scattering, and X-ray circular dichroism signals, will be presented. These studies will be illustrated with applications to solvated molecular systems, intramolecular proton transfer in organic molecules, and chiral molecular systems. Comparisons to experiments will be made where applicable and theoretical predictions will be covered.