Statistical tools for analyzing distributions of rock fabric orientations are limited to point estimators and graphical plots. Inapplicability of conventional statistics is a result of directional nature of these observations. This book presents new techniques expanding arsenal of orientational analysis and applicable in statistics for directional data in general. In the introductory chapter, discussion of directional data is given together with its relation to observations in structural geology. Next chapter presents the tools themselves, starting with point estimation on Stiefel and Grassman manifolds using incomplete data. Following it, a nonlinear regression model of directions on linear (spatial) data is presented. Finally, modification of kernel smoothing for directional data is discussed. Last chapter is a case study of a structurally complex metamorphic terrane in which, besides applying the above tools, use of bootstrap for the purpose of inference is shown. This book should be especially useful for structural geologists specializing in orientational analysis, but may also fit interests of others working with directional data.