I will first overview the classical holomorphic isometry problem between complex manifolds, in particular between bounded symmetric domains. When the source is the unit ball, in general the characterization of holomorphic isometries to bounded symmetric domains is not quite clear. With Shan Tai Chan, we recently characterized the holomorphic isometries from the Poincare disc to the product of the unit disc with the unit ball and it  provided new examples of holomorphic isometries from the Poincare disc into irreducible bounded symmetric domains of rank at least 2.