This chapter addresses the problem of appearance matching, while employing the covariance descriptor. We tackle the extremely challenging case in which the same non-rigid object has to be matched across disjoint camera views. Covariance statistics averaged over a Riemannian manifold are fundamental for designing appearance models invariant to camera changes. We discuss different ways of extracting an object appearance by incorporating various training strategies. Appearance matching is enhanced either by discriminative analysis using images from a single camera or by selecting distinctive features in a covariance metric space employing data from two cameras. By selecting only essential features for a specific class of objects (\textit{e.g.} humans) without defining \textit{a priori} feature vector for extracting covariance, we remove redundancy from the covariance descriptor and ensure low computational cost. Using a feature selection technique instead of learning on a manifold, we avoid the over-fitting problem. The proposed models have been successfully applied to the person re-identification task in which a human appearance has to be matched across non-overlapping cameras. We carry out detailed experiments of the suggested strategies, demonstrating their pros and cons \textit{w.r.t.} recognition rate and suitability to video analytics systems.