  The paper presents a complete (to the best of the author's knowledge)
overview on the existing literature concerning the NLS equation with
point-concentrated nonlinearity. Precisely, it mainly covers the following
topics: definition of the model, weak and strong local well-posedness, global
well-posedness, classification and stability (orbital and asymptotic) of the
standing waves, blow-up analysis and derivation from the standard NLS equation
with shrinking potentials. Also some related problem is mentioned.
