This is a report on Jacobi fields of harmonic maps which focus on their integrability and on their relation with harmonic morphisms. Let \(\phi : (M,g) \to (N,h)\) be a smooth map. Then \(\phi\) is called harmonic if it is an extremal of the energy integral. Several classes of harmonic maps are listed here. The Jacobi operator \(J=\Delta-\text{Ric}\), where \(\Delta\) denotes the Laplacian on sections of \(\phi^{-1}TN\) is a linear elliptic self-adjoint operator; the elements in its kernel are called Jacobi fields along \(\phi\). Some Jacobi fields \(v\) along harmonic maps \(\phi\) are given by one parameter families \(\phi_t\) of harmonic maps with \(\phi_0 = \phi\) and \(v=\partial\phi/\partial t=0\). Conversely, a Jacobi field \(v\) along a harmonic map \(\phi\) is called integrable if it is given in this way. The question, under which conditions all Jacobi fields along a harmonic map are integrable is discussed in depth. When \(\phi\) is a harmonic morphism, some results on Jacobi operators are obtained, illustrated by several examples. A useful list of references is included.