High blood pressure, or hypertension, hasn't required a special issuance (waiver) for a long time! In recent years, if an airman had another medical condition that required a special issuance waiver and also had a history of hypertension on medications, the FAA would add "hypertension on medications" to the special issuance letter.
Around March 2013, the FAA created the Conditions AMEs Can Issue (CACI) category of medical conditions and included hypertension. I wrote an article that explained these, but since questions about hypertension still come up, I will remind you of what is needed.
CACI includes conditions that require airmen to bring some documentation to the AME at each examination for medical certificate renewal. As long as the information fulfills the criteria in the CACI worksheets, the AME can issue an unrestricted medical certificate.
An airman with hypertension who is reporting this to the AME for the first time must provide a letter from the treating physician that informs the FAA when the diagnosis of hypertension was made and contains a comment about significant personal and family history such as a history of heart disease or stroke, a listing of the medications that the airman is taking for the blood pressure, the dosage and frequency of use of each medication, and a mention of any adverse side effects. The letter also should note a couple of blood pressure results taken after the airman has been on the medication(s).
As long as the airman has no effects of hypertension, has been on the medications for at least two weeks without significant side effects, and the blood pressure in the AME's office is less than 155/95, then the AME may issue a medical certificate if the airman is otherwise qualified. The AME does not have to send the records to the FAA, but should maintain them in his or her office records.
For subsequent examinations, the treating physician need only write a letter that informs the FAA how the airman has been doing since the last exam; lists current medications and side effects, if any; and notes blood pressure readings in the office.