In spite of interesting representations of noncompact real Lie groups be typically infinite dimensional, it is hopeless to attempt to classify all of them. In fact, a given representation can be modified in countless ways by simply changing the topology on the representation space, and there are pathological representations, badly behaved, which are unlikely to fit into any reasonable classification scheme. Consequently, the study of the representations of a real semisimple Lie group $G$ is usually restricted to some class, containing the representations which are known to arise in interesting problems and for which there are some hope of a reasonable classification scheme. Harish-Chandra introduced such a class – the class of admissible representations. Harish-Chandra’s strategy to study admissible representations of $G$ was by studying their Harish-Chandra modules. In this talk, we present the classification of irreducible Harish-Chandra modules developed by Beilinson and Bernstein, which is defined by an equivalence of categories between the category of Harish-Chandra modules and the category of coherent sheaves of D-modules on the flag variety of the complexification of the Lie algebra of $G$.