The majority of graph theory research on parameters involved with domination, independence, and irredundance has focused on either sets of vertices or sets of edges; for example, sets of vertices that dominate all other vertices or sets of edges that dominate all other edges. There has been very little research on ``mixing'' vertices and edges. We investigate several new and several little-studied parameters, including vertex-edge domination, vertex-edge irredundance, vertex-edge independence, edge-vertex domination, edge-vertex irredundance, and edge-vertex independence.
