In this talk we present an introduction to integro-differential operators and the obstacle problem, and how they interact with each other in what is known as the fractional obstacle problem. In Rn , the fractional obstacle problem with a given obstacle ϕ ∈ Cc∞ (Rn ) can be written as min{(−∆)s u, u − ϕ} = 0 in Rn . The set {u = ϕ} is called the contact set, and its boundary ∂{u = ϕ} is called the free boundary, which are unknowns of the problem. The free boundary can be divided into two sets: regular points (where it is regular) and degenerate points. In general, degenerate points can exist in any dimension. We will finish the talk by presenting joint results with C. Torres-Latorre on the generic regularity of the free boundary. In particular, in dimension n = 3 we show that the free boundary of almost every solution is formed only of regular points.