On the euclidean plane, conformal maps (that is, angle preserving maps) can be described using complex analysis. This means that after compactifying, conformal maps can be described using algebraic geometry. But what about Minkowski space? As it turns out, there is a nice space of objects called twistors such that automorphisms of this space correspond to conformal maps of (compactified) Minkowski space. In the talk I'll try to define the space of twistors and explain how the geometry of this space relates to the geometry of Minkowski space.