Harmonic maps between Riemannian manifolds extremize a certain natural energy functional generalizing the Dirichlet integral to the setting of Riemannian manifolds. The infinitesimal deformations of harmonic maps are called Jacobi fields. They satisfy a system of partial differential equations given by the linearization of the equations for harmonic maps. The use of twistor methods in the study of both harmonic maps and Jacobi fields has proved quite fruitful, leading to a series of results. We shall describe some aspects of these twistor constructions for harmonic maps and the existing relations with their infinitesimal deformations.