Data is at the heart of the digital revolution. Changing work habits, increasingly stringent electronic record-keeping mandates, and developments in the health care, energy, and retail sectors all suggest a growing demand for data storage and memories for the foreseeable future. Fast, low-power, ultra-high density, and non-volatile magnetic storage and memory systems are projected to accommodate the bulk of the global data storage needs for decades to come and spawn revolutionary data-intensive computing modalities along the way. Their timely development, however, critically depends on the availability of fast and accurate computational tools capable of simulating electromagnetic field and magnetization dynamics in complete magnetic data storage and memory systems. Unfortunately, current simulators are not up to this task. This project focuses on the development of high-performance hybrid micromagnetic-electromagnetic simulators for modeling next-generation magnetic memory and data storage systems. The simulators leverage analytically preconditioned time-domain integral equation methods to solve the Maxwell and Landau-Lifshitz-Gilbert-Slonczewski equations, which govern coupled electromagnetic field and magnetization phenomena. To facilitate the analysis of such phenomena in complex systems involving billions of degrees of freedom, the simulators are implemented on massively parallel Central Processing Unit (CPU) and Graphics Processing Unit (GPU) computers. These simulators are used for the design of next generation magnetic random memory devices as well as bit patterned media and heat-assisted magnetic recording storage systems. Such advanced memory and storage systems are to be essential to future high-performance computing systems.