I will recall quickly the basic facts about classical Bruhat-Tits group schemes over discrete valuation rings, a new approach of mine and Seshadri's, and then introduce the theme of Bruhat-Tits group schemes on higher dimensional bases and my recent work. In a paper in 2012, Pappas and Zhu construct such group schemes in the two dimensional case under some assumptions as the key tool to constructing local models (in the sense of Rapaport and Zink) for PEL Shimura varieties. I will indicate how some recent work of mine on degenerations of Bun(G) connects to the study of local models. The talk will be general and outline the ideas.