  In this paper, we study the nonlinear Schr\"odinger equation with focusing
point nonlinearity in dimension one. First, we establish a scattering criterion
for the equation based on Kenig-Merle's compactness-rigidity argument. Then we
prove the energy scattering below and above the mass-energy threshold. We also
describe the dynamics of solutions with data at the ground state threshold.
Finally, we prove a blow-up criteria for the equation with initial data with
arbitrarily large energy.
