  X-ray speckles have been used for a wide variety of experiments, ranging from
imaging (and tomography), wavefront sensing, spatial coherence measurements all
the way to x-ray photon correlation spectroscopy (XPCS) and ptychography. In
the near-field regime, x-ray speckle-grains preserve shape and size under
free-space propagation for a static random modulation of the illumination,
which permits using them as wavefront markers. The introduction of an object in
the modulated field will lead to a displacement of the speckles due to
refraction. Retrieving the local displacements enables access to the gradient
of the phase-shift induced by the sample. The numerical process to retrieve the
phase information is not trivial and numerous algorithms have been developed in
the past decade with various advantages and limitations. This review focuses on
near-field x-ray speckle phase imaging in the differential mode as described
previously, introducing the existing algorithms with their specifications and
comparing their performances under various experimental conditions.
