Hrushovski constructions are a variant of amalgamation methods. They were invented to construct new examples of strongly minimal theories. The method was later adapted to expansions of fields, including colored fields and powered fields. In this talk, I will present my attempt to apply Hrushovski constructions to ordered fields. I will construct an expansion of RCF by a dense multiplicative subgroup (green points). Hrushovski constructions induce a back-and-forth system, enabling us to study the dp-rank and the open core of this structure. I will also introduce my recent progress on powered fields, an expansion of RCF by "power functions" on the unit circle, and my plan to axiomatize expansions of the real field using Hrushovski constructions.