The crossing number of a graph G, denoted by cr(G), is the minimal number of edge crossings of a "good" drawing of G in the plane. The main motivation is to study the crossing number of the complete graph, as well as the complete bipartite and tripartite graphs. We discuss some famous conjectures on these crossing numbers. We will focus on drawing complete graphs on a cylinder, called circle drawings. This method has been shown by Anthony Hill in 1958 to achieve the conjectured crossing number of the complete graph. Finally, we present new bounds on the tripartite-circle drawings of the complete tripartite graph. This is joint work in progress with J. Diemunsch, S. Fernandez-Merchant, M. Jelic, R. Kirsch, L. Kleist, and E. Matson.