In general most ophthalmologists divide glaucoma into two major categories; open angle and closed angle glaucoma. In angle closure glaucoma, a mechanical problem with the drainage angle of the eye occurs obstructing the drainage angle with the iris, the colored part of the front of the eye.

Acute Angle Closure Glaucoma
Acute closure of the peripheral drainage angle, characterized by a sudden increase in intraocular pressure. Unlike most forms of glaucoma, this type can cause blindness in a matter of hours and can often be prevented or terminated by a sight-saving laser procedure called peripheral laser iridotomy.
Chronic Angle Closure Glaucoma
The iris obstructs the eye’s drainage angle in a slow, progressive fashion. This type of glaucoma is more common in farsighted individuals.
Secondary Angle Closure Glaucoma
Often related to trauma or some other process that causes the lens of the eye to be displaced forward.
 In open angle glaucoma something is wrong with the drainage angle of the eye even though it appears to be open and often appears normal on a microscopic exam, as well.
Primary Open Angle Glaucoma
The drainage angle is open but does not allow fluid to drain adequately for unknown reasons. Many times this type of glaucoma runs in families and is much more common in African Americans.
Low pressure Glaucoma
Glaucoma damage to the optic nerve and vision loss developed despite the intraocular pressure being normal. Sometimes this is found to be related to abnormally thin corneas. Other cases are thought to be related to poor blood flow to the optic nerve because of a variety of conditions including migraine, Raynaud’s disease, heart failure and sleep apnea. Some investigators feel that sometimes this condition does not represent a form of glaucoma at all, but instead a form of slowly progressive anterior ischemic optic neuropthathy (AION).
Congenital Glaucoma
Glaucoma in infants and very young children that occurs because of abnormal development of the drainage angle. The presentation in infants often includes large eyes with cloudy appearing corneas with tearing and light sensitivity. There are many different types of secondary open angle glaucoma.  Usually these result from abnormal deposits of material in the drainage angle, traumatic damage or abnormal blood vessel growth.
Exfoliative Glaucoma
Deposits of a fibrillary material slowly occurs that affects adequate drainage of fluid from the eye. Often occurs in adults of northern European descent.
Pigmentary Glaucoma
Pigment dislodged from the iris affects the eye’s drainage structures. This is one of the few types of glaucoma that occurs in young people, most often young, nearsighted men.
Angle Recession Glaucoma
Scar tissue from previous trauma obstructs the outflow of fluid. Sometimes this type of glaucoma develops years or even decades after the original injury.
Steroid Induced Glaucoma
Intraocular pressure can go up with topical or systemic treatment with steroid medications like prednisone.  Sometimes the pressure rise is high enough or long enough to cause glaucoma-related optic nerve damage and vision loss.
Neovascular Glaucoma
Various disorders, including diabetes, can cause blood vessels to proliferate on the iris and in the eye’s drainage structures obstructing outflow.