Abstract: Holomorphic motions arise naturally in many situations involving complex dynamical systems and are a powerful tool. For example, it has been used by M. Urbanski and A. Zdunik to give a new proof of the real analytic dependence of the Hausdorff dimension of hyperbolic Julia sets (the original approach of Ruelle uses dynamical zeta-functions). I will review the concept of holomorphic motions and some applications to holomorphic dynamics. Then I will consider random dynamical systems and present a version of holomorphic motion of hyperbolic random Julia sets. This is part of actual work with B. Skorulski and M. Urbanski.