In this paper, we study the two dimensional (2D) rotating nonlinear Schrödinger equation with the focusing nonlinearity, modeling the attractive Bose-Einstein condensates (BECs) under a rotating frame. For the 2D case, by employing the Fourier pseudo-spectral method/finite difference methods/time splitting methods, extensive numerical investigations are devoted to the existence/nonexistence of vortices in ground states, dynamics of the center-of-mass, resonance-type phenomenon, vortex stability and blow-up. From our numerical results, we find that there exists no vortex in the ground states of 2D attractive rotating BECs with harmonic traps. Then we focus on the dynamical behavior of the focusing rotating nonlinear Schrödinger equations, which share similar properties to the defocusing case. Finally, we examine numerically the sharp criteria for the blow-up analysis. Extensive numerical tests and theoretical justification are provided.