  General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed
as extensions of Ord's process, are considered. The interaction may occur on
each cell of the tessellation and between neighbour cells. The tessellation may
also be subjected to a geometric hardcore interaction, forcing the cells not to
be too large, too small, or too flat. This setting, natural for applications,
introduces some theoretical difficulties since the interaction is not
necessarily hereditary. Mathematical results available for studying these
models are reviewed and further outcomes are provided. They concern the
existence, the simulation and the estimation of such tessellations. Based on
these results, tools to handle these objects in practice are presented: how to
simulate them, estimate their parameters and validate the fitted model. Some
examples of simulated tessellations are studied in details.
