  The last years have seen striking improvements on Vaisman's question about
existence of locally conformally K\"ahler (lcK) metrics on compact complex
surfaces. The aim of this paper is two-fold. We review results of different
authors which, for all known examples of compact complex surfaces, give a
complete answer to Vaisman's question. We also point out a relation between lcK
surfaces and generalized K\"ahler geometry in four-dimension and prove a new
result concerning generalized K\"ahler structures on Hyperbolic Inoue surfaces.
We conclude with a simple observation on a question of Brunella.
