The EMI (Extracellular space, cell Membrane, and Intracellular space) model provides a microscale framework for simulating cardiac electrical activity, capturing natural discontinuities across domain interfaces and the spatiotemporal evolution of ionic charge distributions on cell membranes. In this work, we investigate scalable preconditioning strategies for the composite Discontinuous Galerkin (DG) discretization of the EMI model, focusing on the generalized Dryja-Smith-Widlund (GDSW) preconditioner and algebraic multigrid (AMG) methods. The GDSW preconditioner is shown to ensure scalability and quasi-optimal convergence, convergence, confirming the theoretical bounds on the condition number, while taylored EMI-AMG preconditioners leverage contemporary computational power for large-scale systems. Numerical experiments demonstrate the robustness of the preconditioners also under ischemic conditions of the in-silico model. Performance evaluations on hybrid CPU-GPU architectures are also discussed, with a comparative analysis of the scalability properties of the two preconditioners, providing critical insights into the effectiveness of multilevel solvers for the EMI model. This talk is part of a joint work with Dr. Ngoc Mai Monica Huynh.