Everybody knows the counting numbers. Most know the integers. Many know the rationals, or reals (even if they call them decimals). Some even know of the complex numbers. But only a few have heard of the p-adic numbers, the final (and most recent) addition to this collection. The p-adic numbers are one of our most important tools in modern number theory, giving us a much clearer perspective on what modular arithmetic really means. This talk hopes to give an elementary introduction into what they are, why they are important and just how weird they can get.