In this talk I will give an introduction to p-adic numbers and the Bruhat-Tits tree (an infinite regular graph without cycles), and show how they naturally lend themselves to the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In the simplest version of "p-adic AdS/CFT", the boundary CFT is defined on the p-adic number field rather than the reals, and the AdS bulk gets replaced by the Bruhat-Tits tree. I will introduce this construction and discuss holographic correlation functions, emphasizing the surprising similarities between the p-adic construction and the standard construction based on real numbers, especially when correlators are expressed in terms of local zeta functions. The ultrametric property of the p-adic norm results in drastic simplifications in the analysis, and I will briefly discuss the simple form of higher-point functions and the operator product algebra, and if time permits, a non-renormalization theorem in p-adic field theories.