Fractional quantum Hall (FQH) systems are among the most intriguing many-particle systems known to physicists, with extremely rich internal structure. One of their most exotic properties is that they support fractionally charged quasiparticles with fractional statistics. Recently there has been very strong interest in the so-called non-Abelian FQH liquids, in which their quasiparticle statistics is non-Abelian, in that the ground state degeneracy of the system grows exponentially with quasiparticle number, and these ground states form non-Abelian representations of the braiding group. Experimental evidence of such exotic statistics remains elusive, but some encouraging progress has been made recently. In this talk we will discuss how one can reveal the non-Abelian statistics experimentally, by probing the FQH liquid in the bulk or at the edge. We showed that bulk thermopower is a promising way to detect the non-Abelian nature, and measure the quantum dimension (a key parameter that quantifies non-Abelian statistics) of these quasiparticles. We also demonstrated a novel cooling effect for such quasiparticles. For the specific candidate system of FQH liquid at filling factor 5/2, we performed numerical calculations that allow for quantitative comparison between theory and on-going edge interference experiments. In particular, we proposed to distinguish the two leading theoretical candidate states, Moore-Read Pfaffian and anti-Pfaffian, using momentum-resolved electron tunneling into the edge, as they have very different edge electron spectral functions.