  The amount and complexity of data delivered by modern galaxy surveys has been
steadily increasing over the past years. Extracting coherent scientific
information from these large and multi-modal data sets remains an open issue
and data driven approaches such as deep learning have rapidly emerged as a
potentially powerful solution to some long lasting challenges. This enthusiasm
is reflected in an unprecedented exponential growth of publications using
neural networks. Half a decade after the first published work in astronomy
mentioning deep learning, we believe it is timely to review what has been the
real impact of this new technology in the field and its potential to solve key
challenges raised by the size and complexity of the new datasets. In this
review we first aim at summarizing the main applications of deep learning for
galaxy surveys that have emerged so far. We then extract the major achievements
and lessons learned and highlight key open questions and limitations. Overall,
state-of-the art deep learning methods are rapidly adopted by the astronomical
community, reflecting a democratization of these methods. We show that the
majority of works using deep learning up to date are oriented to computer
vision tasks. This is also the domain of application where deep learning has
brought the most important breakthroughs so far. We report that the
applications are becoming more diverse and deep learning is used for estimating
galaxy properties, identifying outliers or constraining the cosmological model.
Most of these works remain at the exploratory level. Some common challenges
will most likely need to be addressed before moving to the next phase of
deployment of deep learning in the processing of future surveys; e.g.
uncertainty quantification, interpretability, data labeling and domain shift
issues from training with simulations, which constitutes a common practice in
astronomy.
