I will discuss a few applications of the Klein-Pluecker quadric formalism to geometric incidence problems. It has at least two advantages. The first one is that it enables one to identify quite a few Euclidean 2Dcombinatorial problems, which can be solved by an application of the Guth-Katz theorem for line/line incidences in PR^3, as a hammer. The second one is that it enables one to prove a nontrivial plane-point incidence bound in PF^3, where F is any field. This bound yields new sum-product type results in the case when F has a large positive characteristic.