In hole thismigration presentation, experiments I will discuss performed the theoretical at the LCLS interpretation and FLASHof Xthe -rayrecent free electron laser facilities and targeting the electronic observables, such as timedependent Auger electron signal. I will also describe our progress in developing the ab initio many-electron theoretical tools, such as B-spline ADC, that allow us to gain insight into the mechanisms of the onset and decay of the coherent hole dynamics. Combining application of such ab initio tools with analytical modelling has led us to propose a number of new spectroscopic approaches for direct observation of coherent many-electron dynamics in ionized systems. A central role in the generation of the ionic coherence belongs to the quantum entanglement between the photoelectron and the atomic or molecular ion. We have developed and simulated numerically a Bell test for probing the quantum entanglement in photoionization. We have designed and simulated the quantum protocol for entanglement quantification for the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulses in the strong-field regime, demonstrating robust violation of the Bell inequality. The Bell test developed in our work detects entanglement between the internal states of the Ar+ and the spin states of the photoelectron by exploiting the spin polarization of the photoelectron beam.