Bruhat and Tits associate to a reductive p-adic group a simplicial complex called the Bruhat-Tits building that organizes various structures related to the group, including maximal compact subgroups, their connected variants, integral models, etc. We will give a brief overview of that theory and discuss the analogy with symmetric spaces for real reductive groups, and the relationship to spherical buildings. Speaker(s): Tasho Kaletha (University of Michigan)