Abstract: The famous Hadwiger's Conjecture claims that every graph G has a clique minor as large as its chromatic number. In this talk, I plan to tell you about an immersion-analogue of the Hadwiger's Conjecture. To split off a pair of adjacent edges uv, vw  is to delete both these edges and to add the edge uw, if it is not already present. A graph G is said to contain another graph H as an immersion if H can be obtained from G by iteratively splitting off edges and deleting vertices and edges. The immersion relation is not comparable with the minor relation; however, both well-quasi-order the set of all graphs. I will explain to you some partial results on the immersion-analogue of Hadwiger's Conjecture for certain classes of graphs, such as graphs with no stable set of size three; graphs whose chromatic number equals any of their topological lower bounds; I will determine how large a clique immersion can be guaranteed in a graph arising from each of the four standard graph products of two graphs: Cartesian, direct, lexicographic, and strong. Finally, I will suggest some open problems.