We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang-Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the bijective correspondence between based harmonic spheres in the loop space ΩG of a compact Lie group G and the moduli space of Yang-Mills G-fields on R 4 .