Classification of non-Kahler surfaces and locally conformally Kahler geometry

We give a mostly self-contained proof of the classification of non-Kahler surfaces based on Buchdahl-Lamari theorem. We also prove that all non-Kahler surfaces which are not of class VII are locally conformally Kahler.
Comment: 39 pages, v. 3.0, references added, misprints corrected, several proofs changed in sections 4 and 5. To appear in Russian Math. Surveys