The study of the diversity of multivariate objects shares common characteristics and goals across disciplines, including ecology and organizational management. Nevertheless, subject-matter experts have adopted somewhat separate diversity concepts and analysis techniques, limiting the potential for sharing and comparing across disciplines. Moreover, while large and complex diversity data may benefit from exploratory data analysis, most of the existing techniques emphasize confirmatory analysis based on statistical metrics and models. This work aims to bridge these gaps. First, by cross comparing the analyses of species diversity, microbial diversity, and workgroup diversity, we introduce a framework of diversity concerns aligned across the three areas. The alignment framework is validated and refined by feedback from subject-matter experts. Then, guided by the framework and theoretical information visualization and visual analytics principles (as distinguished from scientific visualization), we propose a unified taxonomy of common analytical tasks for exploration of diversity.