  Photoelectron holography constitutes a powerful tool for the ultrafast
imaging of matter, as it combines high electron currents with subfemtosecond
resolution, and gives information about transition amplitudes and phase shifts.
Similarly to light holography, it uses the phase difference between the probe
and the reference waves associated with qualitatively different ionization
events for the reconstruction of the target and for ascertaining any changes
that may occur. These are major advantages over other attosecond imaging
techniques, which require elaborate interferometric schemes in order to extract
phase differences. For that reason, ultrafast photoelectron holography has
experienced a huge growth in activity, which has led to a vast, but fragmented
landscape. The present review is an organizational effort towards unifying this
landscape. This includes a historic account in which a connection with
laser-induced electron diffraction (LIED) is established, a summary of the main
holographic structures encountered and their underlying physical mechanisms, a
broad discussion of the theoretical methods employed, and of the key challenges
and future possibilities. We delve deeper in our own work, and place a strong
emphasis on quantum interference, and on the residual Coulomb potential.
