  In this paper, we study the global well-posedness of classical solutions to
the 2D compressible MHD equations with large initial data and vacuum. With the
assumption $\mu=const.$ and $\lambda=\rho^\beta,~\beta>1$
(Va\v{i}gant-Kazhikhov Model) for the viscosity coefficients, the global
existence and uniqueness of classical solutions to the initial value problem is
established on the torus $\mathbb{T}^2$ and the whole space $\mathbb{R}^2$
(with vacuum or non-vacuum far fields). These results generalize the previous
ones for the Va\v{i}gant-Kazhikhov model of compressible Navier-Stokes.
