In spite of intense theoretical and experimental efforts over the past years, many features of one-dimensional systems have not yet been clarified. The physics of these systems is dominated by interactions, which are expected to give rise to spectacular phenomena, such as charge fractionalization, fractional statistics, spin-charge separation, and non-Abelian statistics. I will discuss a formalism that allows one to study these phenomena, by analyzing finite-frequency non-symmetrized shot noise. To compute this quantity we use the non-equilibrium perturbative Keldysh formalism. In certain limits some of our results can also be compared with results obtained using integrability. We focus on Fractional Quantum Hall Effect ``Laughlin'' edge states, but our calculations can be extended to carbon nanotubes or to edge states of systems with non-Abelian statistics. The comparison between these results and upcoming measurements can give a definite confirmation of the existence of charge fractionalization, fractional statistics, and non-Abelian statistics in one dimensional systems.