Acoustic neuroma/Vestibular schwannoma
Acoustic neuromas or, more properly, vestibular schwannomas are benign growths of the balance nerves from the inner ear.  They typically grow quite slowly, on the order of 1-2mm per year, and damage both hearing and balance as they do so.  An MRI of the internal auditory canals and brain with and without contrast is required for definitive diagnosis.
 

Smaller, less symptomatic tumors may often be observed with serial MRI scans, especially in patients with limited life expectancy.  Otherwise, vestibular schwannomas are treated with either stereotactic radiosurgery or formal surgical removal.  The likelihoods of tumor control, facial nerve injury, hearing preservation, and functional balance vary considerably with the size and location of the individual tumor, as well as the treatment approach, and so should be discussed with a qualified neurotologist or skull base surgeon.