Faith is an underrated and very valuable currency in the game. It is worth more than per turn gold or production if played correctly. With just 5 Holy Sites there is enough faith income to run holy prayers and “rush” a Great Engineer purchase, like Imhotep or Isoidore. This is just one of the few examples.
Great People / Heroes
In the great people menu, you can use either faith or gold to patronize (buy) a great person. The cost is based on how many points toward that person you already have. I found it easiest to run holy prayer projects to snatch great people I need.
It is often makes sense to build Oracle to get the 25% faith discount when purchasing great people and 15% on recalling Heroes.
Civilian Units
Naturalists and Rock Bands are the units that can be purchased outright as soon as the corresponding civic is unlocked. So need decent culture output to get thee in the first place.
Settlers, Builders, Traders, as well as Archaeologists can be purchased with faith when Monumentality Golden Age dedication is selected. It also provides 30% discount on faith an dgold cost and lasts 3 eras from Classical to Renaissance and plays a huge role in helping the empire expand. Extra movement for builders and settlers also helps to build improvements, chop resources and settle cities x2 faster. It pays to hire Liang as a governor for the extra Builder charge.
Archeologists can also be purchased by Menelik of Ethiopia, as part of the civ ability.
Spies can be purchased by Wu Zetian, as part of leader ablity.
Combat Units
Land combat units can be purchased with faith once the second tier government building is completed – Grand Master’s Chapel.
Naval combat units can be purchased with faith by Gitarja of Indonesia as part of her leader ability.
Nihang unique units can be purchased if you have Lahore city state suzerainty.
Warrior Monks units with Warrior Monks religious belief.
Districts
Districts can be purchased with Moksha’s Divine Architect governor promotion. It often makes sense to build Casa de Contratacion that grants 3 extra governor promotions in addition to other bonuses.
Buildings
Valletta city state suzerainty allows to build Encampment buildings (barracks/stable, armory, military academy) and all city center buildings that include: granary, water mill, monument, walls, sewer and flood barrier.
Jesuit Education religious belief (the only purchase that requires religion founded or converted) allows for purchase of Campus (library, university, research lab) and Theater Square (amphitheater, art/archaeological museum, broadcast center) buildings. It has a strong synergy with District purchasing by Moksha or Reyna, especially for science victory.
Mali can purchase Commercial Hub buildings (market, bank, stock exchange) with faith as part of the civ ability.
Archaeological museum can also be purchased by Menelik of Ethiopia, as part of the civ ability.