This talk will be about the theory of compactification of the character variety. Methods coming from algebraic geometry and tropical geometry can be used to construct and to study some of these compactifications. With these methods it is often possible to get some results by direct computations. We will mostly discuss the special case of deformation spaces of convex real projective structures on open surfaces, a subset of the character variety of the free group in SL(3,R). This is joint work with S. Choi.