In this talk we will discuss quasi-Hitchin representations in Sp(4, C), which are deformations of Fuchsian (and Hitchin) representations which remain Anosov. These representations acts on the space Lag(C4) of complex lagrangian grassmanian subspaces of C4. This theory generalises the classical and important theory of quasi-Fuchsian representations and their action on the Riemann sphere CP 1 = Lag(C2). In the talk, after reviewing the classical theory, we will define Anosov and quasi-Hitchin representations and we will discuss their geometry. In particular, we show that the quotient of the domain of discontinuity for this action is a fiber bundle over the surface and we will describe the fiber. The projection map comes from an interesting parametrization of Lag(C4) as the space of regular ideal hyperbolic tetrahedra and their degenerations. (This is joint work with D. Alessandrini and A. Wienhard.)