The most common late CNS complication of HIV is
CNS involvement in AIDS 

Involvement of the CNS is a common and important manifestation of AIDS.
In addition to the lymphoid system, the nervous system is a major target of HIV infection.
Macrophages and microglial cells in the central nervous system that belong to the monocyte and macrophage lineage are predominant to the types in the brain that are infected with HIV.
It is widely believed that HIV is carried into the brain by infected monocytes.
Ninety per cent of patients demonstrate some form of neurological involvement at autopsy.
In addition to opportunistic infection and neoplasm, several virally determined neuropathological changes occur.

These include

A self limited meningioencephalitis.
Aseptic meningitis
Vascular myelopathy
Peripheral neuropathies and
Most commonly a progressive encephalopathy designated clinically as the AIDS dementia complex. AIDS dementia complex
It is the commonest neurological complication in subacute or chronic HIV encephalitis.
Earlier it was called AIDS encephalopathy or encephalitis.
It present as slowly or rapidly progressive dementia accompanied by abnormalities of motor function.
Dementia
Ataxia
Seizures
Deliruim