An antenna is a structure on your property, so more than radio rules apply to it. In the US three separate layers can limit what you put up: federal rules, state and local government (zoning, permits, building codes), and private agreements such as a homeowners' association or lease. They work differently, and PRB-1 reaches only the second.
Three layers
Federal rules set the baseline, local government regulates land use, and private contracts can be stricter. PRB-1 reaches only the middle layer.
Federal rules apply everywhere. State and local governments then regulate land use. A private contract can be stricter still, and the law treats it differently.
PRB-1 in general terms
PRB-1: not a ban on local rules, not a blank check for them either.
In 1985 the FCC issued a ruling known as PRB-1, reflected in the Part 97 rules. In general terms it says that state and local regulation of amateur antennas must reasonably accommodate amateur radio communications, and must be the minimum practical regulation to achieve a legitimate purpose such as safety or appearance. It does not give you the right to any antenna you like, and it does not exempt you from permits, building codes or reasonable safety rules. A town may regulate, but it must not do so in a way that prevents effective amateur communication. Whether a particular ordinance meets the standard depends on the facts.
Federal rules for tall structures
Not near a public use airport. Near one, lower limits apply.
Separately from local rules, an antenna structure that is more than 200 feet above ground level, or one near a public-use airport, can require notification to the FAA and registration with the FCC. In practice most amateur installations are far below this, but check if you are near an airport.
Private covenants are different
PRB-1 applies to state and local government regulation. Private restrictions such as HOA covenants and deed restrictions are contracts you agreed to when you bought or rented, and are generally enforced as such. Do not assume they are covered by PRB-1; read them before you buy or build. Congress has at times considered legislation on the subject, so check the current position rather than relying on this article.
In practice
Read first: your deed, HOA covenants and local ordinances, before you spend money.
Ask early. A friendly request with a clear description, photos or a drawing, and the safety plan often succeeds where a surprise installation fails. Get any approval in writing.