175 pages ; Graphene is a material consisting of a single layer of carbon atoms, with distinctive electronic characteristics that make it an interesting platform for a variety of applications. In this dissertation, I discuss projects applying graphene towards experiments involving scanning magnetometry, a technique to image stray magnetic fields above the surface of a material or device. First, I provide an overview of scanning magnetometry techniques and detailed fabrication procedures for high-quality graphene devices. Then, I evaluate ultraclean graphene as a material for highly sensitive Hall-effect sensors. These devices are promising for the development of a scanning Hall probe microscope operational over a range of temperatures and magnetic fields not previously accessible with a single sensor. I then discuss calculations predicting an orbital magnetoelectric effect in strained bilayer graphene. This effect is electrically tunable, switchable, and arises from orbital degrees of freedom. Finally, I present progress towards experimentally realizing strained bilayer graphene devices and propose studying the effect using scanning magnetometry.