Computational conformal geometry is an emerging interdisciplinary field, combining modern geometry theories from pure mathematics with computational algorithms from computer science and offering rigorous and practical tools for tackling massive geometric data processing problems. From a theoretical point of view, computational conformal geometry has deep roots in mathematics and physics. In mathematics, it involves fields of algebraic topology, differential geometry, Riemann surface, harmonic analysis, and so on. From a practical point of view, computational conformal geometry offers many powerful tools to handle a broad range of geometric problems in the engineering world. In this talk we briefly introduce related theories and numerical algorithms in practice, including how 3D image data be obtained and the applications on surface morphing by using the Riemann conformal mapping, which reduces a surface matching problem into a unit disk matching problem.