Magnetism plays a significant role in the field of computing, both as a medium on which data is stored, as well a physical phenomenon by which next-generation, non-boolean computation is conducted. Most computing applications that utilize magnetism rely on ferromagnetic materials, electric current-based write methods, and steady-state excitation. While these choices have served us well up to this point, our computing needs are changing more now than ever. The need for more energy efficient computer memory, and the goal of producing powerful next-generation computing architectures like neural networks, require investigation into new magnetic materials, new methods of magnetic control, and new excitation schemes. It is the focus of this dissertation to investigate these topics in the context of three computing applications, image recognition, neuromorphic computing, and magnetic memory. Hardware solutions that are suitable for solving the quadratic optimization problems associated with image recognition are currently under development with the goal of replacing slow, expensive software algorithms. One example utilizes an array of nanomagnetic elements to solve this quadratic optimization problem, but faces an issue of array programmability. Here, dynamic application of spin-orbit torque is investigated as an energy efficient method of magnetic array programmability to enable array re-usability in this non-boolean computing architecture. In the field of neuromorphic computing, there is a need for a high-speed, energy efficient programmable synapse for use in AI systems that must adapt in real-time to continuous data streams. On this front, the utility of a multiferroic antiferromagnetic material is studied, and an upper bound on strain-mediated antiferromagnetic programming is determined. Finally, the last area focused on in this work is magnetic memory. In the current state of the art, magnetic elements with perpendicular anisotropy are switching between binary states using spin-orbit torque. This type of switching requires breaking OOP symmetry, with many mechanisms of symmetry breaking having been proposed. In this work, a symmetry breaking mechanism utilizing intrinsic material properties is studied in combination with voltage-induced strain, with the goal of reducing the dependency on electric current in magnetic memory applications.