Symmetric positive definite matrices, particularly correlation matrices, have become a common source of geometric information in neuroimaging. The challenges encountered with the conventional Euclidean metric have led to the development of alternatives based on Riemannian metrics. Correlation matrices are widely used to describe brain connectivity in anatomical and functional neuroimaging. In this presentation, we will first explore several methods to endow the space of correlation matrices with a differentiable structure. Next, we will present recent Riemannian metrics developed for full-rank correlation matrices and demonstrate how these metrics enable us to perform statistics on non-linear spaces. We will also investigate an expression for the quotient geodesics of the Frobenius metric on covariance matrices and how it translates to full-rank correlation matrices. Finally, we will illustrate our work with applications in the study of brain connectomes, using data obtained from rs-fMRI.