Abstract: Graph drawing in the plane is a well-studied area of research for many years. One particularly interesting drawing of a graph is rectilinear drawing, defined as an embedding of the graph on a plane with vertices placed in general position and edges connecting corresponding vertices as straight line segments. In our works (published in Discrete Applied Mathematics, followed by another accepted article in Computational Geometry: Theory and Applications), we define the d-dimensional rectilinear drawing of a d-uniform hypergraph with n vertices as an embedding of the hypergraph with vertices as points in R^d with and hyperedges drawn as (d−1)-simplices spanned by the d vertices in the corresponding hyperedges. The d-dimensional rectilinear crossing number of a d-uniform hypergraph is defined as the minimum number of crossing pairs of hyperedges among all d-dimensional rectilinear drawings of the hypergraph. In this talk, we will present several results on the d-dimensional rectilinear crossing number of uniform hypergraphs.