In this lecture I'll define relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field over C. We will see that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces, or as certain spaces of valuations. As an application, we will prove thatany separated morphism between quasi-compact and quasi-separated scheme factors as a composition of an affine morphism and a proper morphism. In particular, this gives a new proof of Nagata's compactification theorem. If time permits, I'll try to illustrate analogies between the new spaces and this work, and the non-Archimedean analytic spaces and Raynaud's theory.