The supermassive black hole candidate at the center of our Galaxy (associated with the radio source Sgr A*) is a prime candidate for studying the physical phenomena associated with accretion on to a supermassive black hole. Sgr A* is thought to accrete at an extremely low rate; analogous situations in X-ray binary stars suggest that a jet may be present, making it challenging to formulate a fully self-consistent model that simultaneously explains its spectrum, its variability, its size and its shape. Because Sgr A* is by far the closest supermassive black hole, its expected angular size (the shadow cast from its event horizon) is the largest of any known black hole candidate, making it a prime target for studies using very long baseline interferometry at mm wavelengths, which are capable of reaching spatial resolutions comparable to the expected shadow size.