Focal cerebral ischemia – A stroke occurring in a localized area that can either be acute or transient. This may be due to a variety of medical conditions such as an aneurysm that causes a hemorrhagic stroke, or an occlusion occurring in the affected blood vessels due to a thrombus (thrombotic stroke) or embolus (embolic stroke). Focal cerebral ischemia constitutes a large majority of the clinical cases in stroke pathology with the infarct usually occurring in the middle cerebral artery (MCA). Global cerebral ischemia – A complete stoppage of blood flow to the brain. Cerebral infarction – A "stroke",  caused by complete oxygen deprivation due to an interference in cerebral blood flow which affects multiple areas of the brain.Cerebral hypoxia can also be classified by the cause of the reduced brain oxygen:
Hypoxic hypoxia – Limited oxygen in the environment causes reduced brain function. Divers, aviators, mountain climbers, and fire fighters are all at risk for this kind of cerebral hypoxia. The term also includes oxygen deprivation due to obstructions in the lungs. Choking, strangulation, the crushing of the windpipe all cause this sort of hypoxia. Severe asthmatics may also experience symptoms of hypoxic hypoxia. Hypemic hypoxia – Reduced brain function is caused by inadequate oxygen in the blood despite adequate environmental oxygen. Anemia and carbon monoxide poisoning are common causes of hypemic hypoxia. Ischemic hypoxia ( or "stagnant hypoxia") – Reduced brain oxygen is caused by inadequate blood flow to the brain. Stroke, shock, cardiac arrest and heart attack may cause stagnant hypoxia.
Problems during labor and delivery can include umbilical cord occlusion, torsion or prolapse, rupture of the placenta or uterus, excessive bleeding from the placenta, abnormal fetal position such as the breech position, prolonged late stages of labor, or very low blood pressure in the mother. Problems after delivery can include severe prematurity, severe lung or heart disease, serious infections, trauma to the brain or skull, congenital malformations of the brain or very low blood pressure in the baby and due to suffocation in cases of Münchausen syndrome by proxy.The severity of a neonatal hypoxic-ischaemic brain injury may be assessed using Sarnat staging, which is based on clinical presentation and EEG findings, and also using MRI. Signs and symptoms of HIE may include:

Low Apgar scores, <5 at 5 minutes and 10 minutes. Floppiness, or unreactive to sights or sounds, or more tense and agitated. Low heart rate. Low blood pressure. Poor muscle tone and absent reflexes. Weak breathing, no breathing at all, or rapid breathing. Need for resuscitation after delivery. Weak cry. Bluish or pale skin color. Excessive acid in the blood. Seizures or abnormal movements. Problems feeding

Mechanism
Details of the mechanism of damage from cerebral hypoxia, along with anoxic depolarization, can be found here: Mechanism of anoxic depolarization in the brain

Diagnosis
Classification
Cerebral hypoxia is typically grouped into four categories depending on the severity and location of the brains oxygen deprivation:

Diffuse cerebral hypoxia – A mild to moderate impairment of brain function due to low oxygen levels in the blood.