Do not place extremely hot pots or pans on brass trivets. Brass conducts heat and there is a risk of damaging sensitive surfaces.
The surface of brass is sensitive to objects that can scratch and mar it as well as certain polishing cloths and sponges. Candle wax and grease can be washed off with hot water and then polished with a soft cloth. Avoid using brushes, steel wool and the like.
Unpolished brass will become darker over time from exposure to air. This change can be beautiful. If the surface is affected by grease such as fingerprints and candle wax, or by other corroding substances, it can eventually be damaged and more difficult to polish away. This can happen especially in a humid environment.