  This work presents a review of the current state of research in data-driven
turbulence closure modeling. It offers a perspective on the challenges and open
issues, but also on the advantages and promises of machine learning methods
applied to parameter estimation, model identification, closure term
reconstruction and beyond, mostly from the perspective of Large Eddy Simulation
and related techniques. We stress that consistency of the training data, the
model, the underlying physics and the discretization is a key issue that needs
to be considered for a successful ML-augmented modeling strategy. In order to
make the discussion useful for non-experts in either field, we introduce both
the modeling problem in turbulence as well as the prominent ML paradigms and
methods in a concise and self-consistent manner. Following, we present a survey
of the current data-driven model concepts and methods, highlight important
developments and put them into the context of the discussed challenges.
