  We overview our recent work defining and studying normal crossings varieties
and subvarieties in symplectic topology. This work answers a question of Gromov
on the feasibility of introducing singular (sub)varieties into symplectic
topology in the case of normal crossings singularities. It also provides a
necessary and sufficient condition for smoothing normal crossings symplectic
varieties. In addition, we explain some connections with other areas of
mathematics and discuss a few directions for further research.
