  The electron microscope has been a powerful, highly versatile workhorse in
the fields of material and surface science, micro and nanotechnology, biology
and geology, for nearly 80 years. The advent of two-dimensional materials opens
new possibilities for realising an analogy to electron microscopy in the solid
state. Here we provide a perspective view on how a two-dimensional (2D) Dirac
fermion-based microscope can be realistically implemented and operated, using
graphene as a vacuum chamber for ballistic electrons. We use semiclassical
simulations to propose concrete architectures and design rules of 2D electron
guns, deflectors, tunable lenses and various detectors. The simulations show
how simple objects can be imaged with well-controlled and collimated in-plane
beams consisting of relativistic charge carriers. Finally, we discuss the
potential of such microscopes for investigating edges, terminations and
defects, as well as interfaces, including external nanoscale structures such as
adsorbed molecules, nanoparticles or quantum dots.
