We consider the generalized Benjamin-Ono (gBO) equation on the real line, ut+∂x(−Hux+1mum)=0,x∈R,m=2,3,4,5, and perform numerical study of its solutions. We first compute the ground state solution to −Q−HQ′+1mQm=0 via Petviashvili's iteration method. We then investigate the behavior of solutions in the Benjamin-Ono (m=2) equation for initial data with different decay rates and show decoupling of the solution into a soliton and radiation, thus, providing confirmation to the soliton resolution conjecture in that equation. In the mBO equation (m=3), which is L2-critical, we investigate solutions close to the ground state mass, and, in particular, we observe the formation of stable blow-up above it. Finally, we focus on the L2-supercritical gBO equation with m=4,5. In that case we investigate the global vs finite time existence of solutions, and give numerical confirmation for the dichotomy conjecture, in particular, exhibiting blow-up phenomena in the supercritical setting.