  Twistor methods provide a powerful tool in the study of harmonic maps and
harmonic morphisms. Indeed, their use has enabled us to produce a variety of
examples of harmonic morphisms defined on 4-dimensional manifolds, and a
complete classification in some cases. In the first part of this work, we
generalize those constructions to obtain harmonic morphisms from
higher-dimensional manifolds. The use of twistor methods in the study of Jacobi
fields has proved quite fruitful, leading to a series of results. In the second
part of this work we give a general treatment of the relations between Jacobi
fields and variations in the twistor space, obtaining first-order analogues of
twistorial constructions.
