A Lie bialgebra is a pair (g,δ), where g is a Lie algebra and δ : g -> g ∧ g is a map, a so-called cocommutator, that is closed relative to the Chevalley--Eilenberg cohomology of g ∧ g-valued forms and whose transpose induces a Lie algebra structure on g^*. If δ(·) = [·,r]_S for a bivector r ∈ g ∧ g and [·,·]_S is the Schouten—Nijenhuis bracket, the Lie bialgebra (g,δ) is called coboundary. The classification of coboundary Lie bialgebras is carried out generally through ad-hoc methods to solve the modified Yang—Baxter equations determining all possible r. In this talk, I will present several much more unifying approaches to classifying three-dimensional real coboundary Lie bialgebras by extending Lie-algebra theory techniques to Grassmann algebras. To illustrate our techniques, several examples will be discussed.