Biodiversity is a crucial part of nature's precious assets that provide many human needs and insures against environmental disasters. Scientists have not yet reached a consensus on the definition of biodiversity; we will, therefore, discuss a variety of interpretations. Most biodiversity studies have focused on species diversity, but biodiversity has a more comprehensive aspect. Due to the extinction of plant and animal species, climate change, air pollution, advances in technology and industry, development of agricultural and urban lands, and changing human attitudes toward species, ecosystems, and landscapes, biodiversity has become a more attractive topic for researchers over the last decade. When diversity is being measured, a precise taxonomic classification of the subject must be made. Although many diversity indices and models have been proposed to quantify diversity, many of them confuse researchers. The use of new approaches, such as taking into account functional and genetic characteristics (functional diversity and phylogenetic diversity, respectively) has revealed hidden functions, services, and sustainability of ecosystems. These valuable measures have also created new issues. The variety of introduced indices, as well as the multidimensionality of ecosystem services and the different roles of species in different ecosystem functions, have raised new questions and numerous complexities. Therefore, researchers have tended to use multidimensional and trans-ecosystem approaches. In this review article, first, the definitions and concepts of biodiversity and its historical background are presented, and then new ideas, challenges, and opportunities are discussed.