One of the most basic and fundamental problems in the representation theory of real reductive groups is to classify the irreducible representations. Following the ideal of introducing homology and homotopy groups to a topological space, one can also attach certain invariants to irreducible representations, such as infinitesimal characters, Berstein degree, Gelfand-Kirillov dimension, K-types, associated cycles, wavefront cycles. In this talk, I will introduce some of these invariants, describe their relations, show the strategy on how to compute these invariants explicitly.