Serious complications are rare. However, an untreated sinus infection can spread to other areas in the skull.
The sinuses around the eye and the brain are separated by just a thin membrane. So, if the infection spreads to the passages around the eye, it could also penetrate through the membrane of the brain, causing [simple_tooltip text=meningitis tooltip=An inflammation of the membrane surrounding the brain and spinal cord due to an infection, injury, specific medicines, or cancer. ].
Infection in the bones is called osteomyelitis.
Infection in the tissues surrounding the eyes is called orbital cellulitis.