The polynomial method has many applications in finite geometry, for example for (multiple) blocking sets, arcs, caps, (k,n)-arcs, and other substructures of finite affine or projective spaces. In this talk a small part of the applications is selected: applications of fully reducible lacunary polynomials over finite fields. Such polynomials were Introduced by Laszlo Redei in the 70’s and he applied them to the problem of directions determined by a set of $q$ points in a Desarguesian affine plane. In this talk we briefly survey the main theorems of Redei’s book and some more recent applications of fully reducible lacinary polynomials in finite geometry. These results are mostly related to generalizations of the above mentioned direction problem and blocking sets.