Most of past and current researches on chemotaxis models deal with attraction and repulsion separately. But in some biological processes (or experiments), the repulsive process often follows the attractive process for balance in order to accomplish some biological objects. Hence an attraction and repulsion chemotaxis model will be more realistic than a sole attraction or repulsion chemotaxis model in this scenario. In this talk, we shall present the first mathematical results on an attraction-repulsion chemotaxis model and show the interplay of these two opposed and competing biological processes. Pattern formations will be shown and various open questions will be presented.