  Major advances in X-ray sources including the development of circularly
polarized and orbital angular momentum pulses make it possible to probe matter
chirality at unprecedented energy regimes and with Angstr\"om and femtosecond
spatiotemporal resolutions. We survey the theory of stationary and
time-resolved nonlinear chiral measurements that can be carried out in the
X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron)
facilities. A variety of possible signals and their information content are
surveyed.
