A blocking set in a plane is a set of points that meets every line. It is called non-trivial if it does not contain a line. A blocking set is minimal if it is minimal subject to set theoretical inclusion. There are classical results on the possible sizes of minimal blocking sets, due to Bruen, Bruen-Thas, Blokhuis, Ball Gacs, Sziklai and the speaker. We will try to survey these result. An almost blocking set is a set of points which “almost” meets all lines, that is there are only few lines that are disjoint from it. We will show some conditions (specify what “few” means) that guarantee that an almost blocking set can be obtained from a blocking by deleting not too many points. Again, there are some old results by Erdos and Lovasz in this directions. We will mention recent such results by Zsuzsa Weiner and the speaker.