If T is a self-adjoint operator on a finite-dimensional Hilbert space H, then any vector v in H can be written as a linear combination of eigenfunctions of T. The concept of eigenfunction expansion is the generalization of this fact to infinite-dimensional Hilbert spaces. In this talk, we introduce this concept in the specific case of Jacobi operators on \ell^2(\mathbb{Z}). In particular, we will present the connection between eigenfunction expansion and subordinacy theory, which relates asymptotic properties of solutions to the eigenvalue equation to singularity properties of spectral measures.