This review presents recent work carried out at the Landau Institute for Theoretical Physics of the Russian Academy of Sciences on the study of the effect of superconducting vortices on the shape and position of Néel-type skyrmions in superconductor—chiral ferromagnet heterostructures. Based on analytical and numerical approaches, a number of effects caused by the inhomogeneous magnetic field of the vortex have been predicted: a significant increase in the skyrmion radius, a change in its chi„rality in the case of a coaxial configuration of the vortex and skyrmion, and modification of the skyrmion shape in the case of an eccentric configuration. Recent experiments studying these effects are discussed.