I assume that you are interested in gas turbine (GT) air seals.  Mostly they are labyrinth seals and I would dare to say that they are more air flow metering features (like some strange kind of metering orifices) than seals.  In fact those seals meters portion of the compressed air flow, which is utilized to prevent oil leak (from main bearings) into main air stream and for cooling purposes (bearing and hot section cooling).  For such application once upon a time (some 25 years ago) RR tested those brush seals (carbon fibre brush) but it seems that they were not so successful or they would have been widely used until now.  Therefore labyrinth seals are still the best.

There is another GT compressor region requiring close gap control and that is blade tip clearance.  Similar situation is with turbine blade clearance but technically even worse since very hot exhaust gases have to be sealed.  The compressor clearance control is usually achieved by using some abradable (not abra-ka-dabra) coatings minimizing the gap and naturally the blade tips are machined, in assembly, to rather accurate diameter.  They are allowed to rub the coating initially (part of assembly procedure) and that is how min clearance is achieved.  Not all GT compressors are with such coatings.  Many designers and manufacturers consider that keeping manufacturing tolerances close enough will keep those clearances small enough.  Ideally they should be of the order of boundary layer thickness.

Regarding turbine section there are:
- labyrinth seals at blade tips (a tip platform-shroud is integral part of the blade casting, lab seal teeth are machined in the platform and when assembled an outer rim is formed, which with a turbine casing forms a lab seal, unfortunately such blades are more prone to creep damage)
- abradable coatings (significantly differing from compressor casing coatings) or honeycomb shrouds sustaining high temperatures and not damaging the blades when blades rub on them

Unfortunately I didn’t find any good web site dealing wit this matter.  I also ran into that information that NASA tested brush seal in GEAE T-700 turbine section as a means of reducing blade tip clearance or better to say to reduce blade tip loss.  I would say tested as a substitution for hot section abradable coatings.