Spline surfaces defined on planar domains have been studied for more than 40 years and universally recognized as highly effective tools in approximation theory, computer-aided geometric design, computer-aided design, computer graphics and solutions of differential equations. Many methods and theories of bivariate polynomial splines on planar triangulations carry over. However, spherical Bezier-Bernstein polynomial splines defined on sphere have several significant differences from them because sphere is a closed manifold much different from planar domains. This book is based on the dissertation completed in the University of Georgia. It includes following contents: an overview of spherical splines, the method to construct a unique spherical Hermite interpolation splines by using minimal energy method, the estimation of approximation order under L2 and L-infinity norms, methods of hole filling and scattered data fitting with global r-th order continuity. Many examples in this book have demonstrated our theories and applications. This book is especially useful for people who have interest in CAGD, CAD & CG, multivariate splines, geoscience and spline finite element methods.