Abstract: We survey some classical Erdos-type problems about configurations of points and lines in the plane and higher dimensions. We present some recent solutions to old conjectures among which are Scott's conjecture from 1970 about the minimum number of directions determined by $n$ points in three dimensions, two conjectures of Bezdek from around 1990 about unit circles in the plane, a conjecture of Murty from 1971 about magic configurations of points in the plane, and a conjecture of Erdos, Purdy, and Strauss (1977) about the minimum number of distinct areas of triangles determined by n points in the plane. Since some of the problems we discuss are dated back to the 19'th century, we will assume no prior knowledge and the talk should be accessible to a wide audience.