In 2005, the FLASH soft X-ray free-electron laser (FEL) in Hamburg, Germany, achieved its first lasing, which began an intensive phase of global FEL construction. Subsequently, the United States, Japan, South Korea, China, Italy, and Switzerland all began building such photon facilities. Recently, the new generation of FEL has started to utilize superconducting acceleration technology to achieve high-repetition-rate pulse output, thereby improving experimental efficiency. Currently completed facility is the European XFEL, ongoing constructions are the LCLS-II in the United States and the SHINE facility in Shanghai, and the facility in preparation is the Shenzhen superconducting soft X-ray free-electron laser ((SFEL)-F-3). These FEL facilities generate coherent and tunable ultrashort pulses ranging from the extreme ultraviolet to hard X-ray spectrum, which advances the FEL-based scattering techniques such as ultrafast X-ray scattering, spectroscopy, and X-ray nonlinear optics, thereby transforming the way we study correlated quantum materials on an ultrafast timescale. The self-amplified spontaneous emission (SASE) process in FEL leads to timing jitter between FEL pulses and the synchronized pump laser, influencing the accuracy of ultrafast time-resolved measurements. To address this issue, timing tools have been developed to measure these jitters and reindexed each pump-probe signal after measurement. This success enables ultrafast X-ray diffraction (UXRD) to be first realized, and a systematic study of Peierls distorted materials is demonstrated. In addition, the high flux of FEL pulses enables Fourier transform inelastic X-ray scattering (FT-IXS) method, which can extract the phonon dispersion curve of the entire Brillouin zone by performing the Fourier transform on the measured momentum dependent coherent phonon scattering signals, even when the system is in a non-equilibrium state. The UXRD is typically used to study ultrafast lattice dynamics, which requires hard X-ray wavelengths. In contrast, time resolved resonant elastic X-ray scattering (tr-REXS) in the soft X-ray regime has become a standard method of investigating nano-sized charge and spin orders in correlated quantum materials on an ultrafast time scale. In correlated quantum materials, the interplay between electron dynamics and lattice dynamics represents another important research direction. In addition to Zhi-Xun Shen's successful demonstration of the combined tr-ARPES and UXRD method at SLAC, this paper also reports the attempts to integrate UXRD with resonant X-ray emission spectroscopy (RXES) for the simultaneous measurement of electronic and lattice dynamics. Resonant inelastic X-ray scattering (RIXS) is a powerful tool for studying elementary and collective excitations in correlated quantum materials. However, in FEL-based soft X-ray spectroscopy, the wavefront tilt introduced by the widely used grating monochromators inevitably stretches the FEL pulses, which degrades the time resolution. Therefore, the new design at FEL beamlines adopts low line density gratings with long exit arms to reduce pulse stretch and achieve relatively high energy resolution. For example, the Heisenberg-RIXS instrument at the European XFEL achieves an energy resolution of 92 meV at the Cu L-3 edge and approximately 150 fs time resolution. In recent years, scientists at SwissFEL's Furka station have drawn inspiration from femtosecond optical covariance spectroscopy to propose a new method of generating two-dimensional time-resolved resonant inelastic X-ray scattering (2D tr-RIXS) spectra. This method involves real-time detection of single-shot FEL incident and scattered spectra, followed by deconvolution calculation to avoid photon waste and wavefront tilt caused by monochromator slits. The SQS experimental station at European XFEL, built in 2023, features a 1D-XUV spectrometer that utilizes subtle variations in photon energy absorption across the sample to induce spatial energy dispersion. Using Wolter mirrors, it directly images spatially resolved fluorescence emission from the sample onto the detector to generate 2D tr-RIXS spectra without the need for deconvolution. However, this design is limited to specific samples. Currently, the S3FEL under designing has a novel 2D tr-RIXS instrument that uses an upstream low line density grating monochromator to generate spatial dispersion of the beam spot, allowing the full bandwidth of SASE to project spatially dispersed photon energy onto the sample. Subsequently, an optical design similar to the 1D-XUV spectrometer will be employed to achieve 2D tr-RIXS spectra, thereby expanding the applicability beyond specific liquid samples. These new instruments are designed to minimize pulse elongation by fully utilizing SASE's full bandwidth, approaching Fourier-transform-limited RIXS spectra in both time and energy resolution. Nonlinear X-ray optical techniques, such as sum-frequency generation (SFG) and second-harmonic generation, are adapting to X-ray wavelengths and opening up new avenues for detecting elementary excitations. The X-ray transient grating spectroscopy extends its capabilities to studying charge transport and spin dynamics on an ultrafast timescale. The future development of these scattering methods provides unique opportunities for detecting dynamical events in various systems, including surface and interface processes, chirality, nanoscale transport, and so-called multidimensional core-level spectroscopy.
