A few introductory remarks on line arrangements

Points and lines can be regarded as the simplest geometrical objects. Incidence relations between them have been studied since ancient times. Strangely enough our knowledge of this area of mathematics is still far from being complete. In fact a number of interesting and apparently difficult conjectures has been raised just recently. Additionally a number of interesting connections to other branches of mathematics have been established. This is an attempt to record some of these recent developments.