Polarimetry encompasses a collection of optical techniques broadly used in a variety of fields. Nowadays, such techniques have provided their suitability in the biomedical field through the study of the polarimetric response of biological samples (retardance, dichroism and depolarization) by measuring certain polarimetric observables. One of these features, depolarization, is mainly produced by scattering on samples, which is a predominant effect in turbid media as biological tissues. In turn, retardance and dichroic effects are produced by tissue anisotropies and can lead to depolarization too. Since depolarization is a predominant effect in tissue samples, we focus on studying different depolarization metrics for biomedical applications. We report the suitability of a set of depolarizing observables, the indices of polarimetric purity (IPPs), for biological tissue inspection. We review some results where we demonstrate that IPPs lead to better performance than the depolarization index, which is a well-established and commonly used depolarization observable in the literature. We also provide how IPPs are able to significantly enhance contrast between different tissue structures and even to reveal structures hidden by using standard intensity images. Finally, we also explore the classificatory potential of IPPs and other depolarizing observables for the discrimination of different tissues obtained from ex vivo chicken samples (muscle, tendon, myotendinous junction and bone), reaching accurate models for tissue classification.