In this talk we give a modern presentation of the "ergodic method" of Linnik on the distribution of representations of large integers by ternary quadratic forms. Specifically we will describe the works of Linnik and Skubenko on the distribution of quadratic cycles (i.e. Heegner points or closed geodesics) on modular curves. If time permit we will describe some new development suggested by the method and by recent progress in ergodic theory. This is joint work with M. Einsiedler, E. Lindenstrauss and A. Venkatesh.