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Anosov groups constitute a rich class of discrete subgroups of Lie groups, offering both geometric and dynamical intricacies. This class of discrete groups also have deep connections with several current developments in mathematics, such as higher Teichmüller theory and thin groups. For a semisimple Lie group G, each conjugacy class of parabolic subgroups P of G gives rise to a family of Anosov subgroups known as P-Anosov. A natural inquiry is: Which abstract groups can arise as P-Anosov subgroups of G? In this talk, we will discuss some results that fully address this question for many specific pairs of G and P. This talk will be partly based on joint work with Z. Greenberg and J.M. Riestenberg.