A new general method of ``score matching estimation'' (SME) will be presented on a compact oriented Riemannian manifold. Particular cases include many key directional and shape analysis distributions such as von Mises-Fisher, Bingham and preshape distributions. The estimator has many properties such as asymptotically normality. Further, the beauty of the estimator is that it is easy to compute as a solution of a linear set of equations and requires no knowledge of the normalizing constant. This property makes the estimator amenable for streaming data. Some examples will be given to demonstrate its good performance; in general, there is a little loss of efficiency. Challenging applications from structural molecular biology related to protein and RNA will be presented in the talk.