In late 1980’s Margulis completed the proof of “Oppenheim Conjecture”, i.e. if Q is a real, non-degenerate, indefinite quadratic form in n>=3 variables, and Q is not a scalar multiple of a form with integer coefficients, then 0 is in the closure of the set of real numbers Q(Z^n\{0}). In fact it turns out that in this case Q(Z^n\{0}) is dense in the real line. The proof involves the study of the action of a certain subgroup of SL(3, R) on the homogeneous space SL(3, R)/SL(3, Z), more precisely, the closure of every orbit of such action is a nice geometric subset of SL(3, R)/SL(3,Z). This topological feature was broadly generalized by Ratner, and the classification of the invariant ergodic measures plays a decisive role in her approach. The aim of this talk is to briefly discuss these ideas and related examples, hopefully we will come to the sketch of the proof of some special case of measure classification.