The compressible ideal MHD equations contain two small parameters , such as Mach number and Alfvén number. When these two parameters are considered to have fixed ratios to one another then the system has two time scales: one induced by the terms containing the small parameters and the other coming from the order-one terms in the equation. The system has three time scales as two physical parameters tend to zero in a different manner. The recent results on both two-scale and three-scale limits of the compressible ideal MHD equations will be presented in the talk and it demonstrate that the issue of three-scale singular limits is much more complicated than for the classical two-scale singular limits.