  For more that seventy years, the measurements of fluxes of galaxies at
different wavelengths and derived colours have been used to estimate their
corresponding cosmological distances. From the fields of galaxy and AGN
evolution to precision cosmology, the number of scientific projects relying on
such distance measurements, called photometric redshifts, have exploded. The
benefits of photometric redshifts is that all sources detected in photometric
images can have some distance estimates relatively cheaply. The major drawback
is that these cheap estimates have a low precision when compared with the
resource-expensive spectroscopy. The methodology to estimate redshifts has been
through several major revolutions throughout the last decades, triggered by
increasingly more stringent requirements on the photometric redshift accuracy.
Here, we review the various techniques to obtain photometric redshifts, from
template-fitting to machine learning and hybrid systems. We also describe the
state-of-the-art results on current extra-galactic samples and explain how
survey strategy choices impact redshift accuracy. We close the review with a
description of the photometric redshifts efforts planned for upcoming wide
field surveys, which will collect data on billions of galaxies, aiming to solve
the most exciting cosmological and astrophysical questions of today.
