## 1 Introduction  
The X-ray absorption fine structure (XAFS) method has been developed over the past half century according to the progress of X-ray sources. In particular, its time resolution has been improved significantly. In the early days of XAFS experiments (i.e., in the 1970s before the birth of synchrotron radiation (SR) facilities), it took a couple of days or more than a week to obtain a XAFS spectrum with a good signal-to-noise (S/N) ratio due to the low X-ray flux of standard X-ray tubes. SR facilities were the first game-changer to make the measurement time of XAFS much shorter. It became possible to measure an XAFS spectrum with a good S/N ratio in less than 1 h in the 1980s using SR facilities. Further progress was achieved by the development of fast data acquisition techniques such as quick XAFS (QXAFS) [1] and dispersive XAFS (DXAFS) [2], which improved the time resolution down to the millisecond region in the 1990s. It is presently possible to measure an XAFS spectrum with a time resolution equal to or less than millisecond order [3; 4]. Although the time resolution of XAFS has been reduced by an order of approximately \(10^{8}\) compared to its early days, it is usually limited by the physical motion of X-ray optics for QXAFS or the response of data acquisition systems for QXAFS and DXAFS. Although there were transient XAFS methods to observe faster phenomena that happen within an order of milliseconds [5; 6; 7], it was difficult to reduce the time resolution below a single nanosecond. To go beyond this limitation, the pump-probe XAFS method was developed in the early 2000s, and could provide dynamics of materials in a time resolution of nanoseconds or less [8; 9; 10; 11; 12]. X-rays coming from an SR are pulses with finite pulse width (typically ca. 100 ps). Such a short pulse feature enables the dynamics of materials to be tracked during the photoinduced states by XAFS spectra as a function of the delay time between the pump (excitation) and the probe (detection). The time resolution in SR facilities is limited by the pulse duration of the X-ray pulse because the pulse duration of an excitation laser (100 fs) is typically much shorter than the X-ray pulse duration (ca. 100 ps). The advent of very short pulse X-ray sources such as the X-ray free electron laser (XFEL) has extended the horizon of the pump-probe XAFS to the femtosecond region [13]. The high peak intensity enables the application of XAFS techniques such as high energy resolution fluorescence detected X-ray absorption near edge structure (HERFD-XAFS) [14; 15] or resonant inelastic X-ray spectroscopy (RXS) [16; 17; 18]. In this short review, we describe our studies on the photoexcitation processes of the tungsten trioxide (WO\({}_{3}\)) and bismuth vanadate (BiVO\({}_{4}\)) photocatalysts by pump-probe XAFS in SR and XFEL [19; 20; 21; 22] over the last decade. The behavior of photocarriers in photocatalysts has been discussed in terms of band theory. The electron in the valence band mainly composed of oxygen atoms is photoexcited to the conduction band mainly composed of cations. The created photocarriers (electron in the conduction band or hole in the valence band) travel to the surface and react with substances [23; 24; 25]. Most experimental data have been obtained by optical spectroscopic techniques, which provide information regarding the energy levels of photocarriers in the reciprocal space (k-space). On the other hand, the location of photocarriers in real-space (r-space) has rarely been discussed based on the direct observation of photocatalysts after photoexcitation. XAFS provides information on the local electronic and geometrical structures around the X-ray absorbing atom. Therefore, XAFS can address photocarrier dynamics in the r-space around the X-ray absorbing atom [15; 26; 27]. WO\({}_{3}\) and BiVO\({}_{4}\), to which we have applied the pump-probe XAFS, comprise a Z-scheme photocatalyst system that mimics a photosynthesis system [28; 29; 30].