Pantheons provide basic bonuses for cities, usually based on terrain, resources, or buildings. You may found a Pantheon once you've accumulate 50 Faith.
Note that if a bonus applies to a particular resource (Gold, Wine, etc.), the bonus will work regardless of whether the resource is improved or not. On the other hand, bonuses applying to particular improvements (Plantation, Pasture, etc.) will work as long as the improvement is not pillaged. Terrain bonuses always apply as long as you don't change the terrain - for example, by cutting down the jungle in a tile.
+1 Faith for every 3 Citizens in a city; +2 Culture from Councils.
+1 Faith and Gold from Mines on improved resources, and +3 Production from Monuments.
God of All Creation
2 Faith in Capital; +1 Culture and +1 Happiness for every Pantheon ever founded (capping at 8).
God of Commerce
+1 Faith for every +25 Gold per turn you produce; +2 Faith and +2 Gold in Cities with a City Connection.
God of Craftsmen
+1 Production and Gold from Quarries and Stone Works, and +3 Faith in cities with a Specialist.
God of the Expanse
+25% faster border growth, and gain 20 Faith every time a city expands its borders. Bonus scales with Gamespeed.
God of the Open Sky
+1 Culture for every 2 Plains or Grassland tiles (without hills or features) worked by a City; +1 Faith and +1 Gold from Pastures.
God of the Sea
+1 Faith and Production from Fishing Boats and Atolls; +3 Food in coastal Cities.
God of the Stars and Sky
+1 Faith, +1 Culture, and +2 Production from Tundra tiles with improved resources.
God of the Sun
+2 Food, +1 Gold from Granaries. +1 Faith and +2 Culture from Farms on Wheat
God of War
+50% increase in City Ranged Combat Strength, and gain Faith if you win a battle.
+1 Culture, Faith, Gold, and Science for every 5 Followers of your Pantheon in owned cities.
Goddess of Beauty
+2 Faith from World Wonders. Ignore 'Number of Policies Needed' requirement for Pre-Renaissance Wonders.
Goddess of Fertility
+1 Food and Faith from Shrines, Watermills, and Wells. 15% faster Growth Rate.
Goddess of Festivals
+1 Faith, +2 Culture and +2 Gold for every unique Luxury Resource you control.
Goddess of Love
Gain 12 Faith and Golden Age Points every time a Citizen is born. Bonus scales with Era and Gamespeed.
Goddess of Nature
+1 Faith and +1 Culture for every 2 Mountains within 3 tiles of a City (capping at the City's population). Natural Wonders gain +3 Faith and +2 Culture.
Goddess of Protection
+10 HP healed per turn in friendly territory. +1 Faith and Culture from Palace, Walls and Barracks.
Goddess of Purity
+1 Faith and Food from Oases, Lakes, and Marshes. +1 Happiness from Cities on rivers.
Goddess of Renewal
+1 Faith and Culture for every 2 Jungle or 2 Forest tiles worked by a City. +1 Science and Faith from Herbalists.
Goddess of Springtime
+1 Gold, Food, and Culture from Plantations, and +2 Faith from Markets.
Goddess of the Hunt
+1 Faith, Food and Culture from Camps.
Goddess of Wisdom
+1 Faith for every 15 Science per turn. +2 Science and +1 Faith in every City.
Spirit of the Desert
+2 Faith, +2 Gold, and +1 Food from Desert tiles with Improved resources.
You may choose one of these beliefs when founding a Religion, and these affect only the Founder/Owner of the Holy City.
Each Founder has a National Wonder associated with it that can be built when a certain % of the World Population follows your Religion. Constructing this Wonder allows the founder/Owner to select a Reformation Belief.
Unlocks Apostolic Palace National Wonder (+4 Faith, +4 Golden Age Points; +5 Golden Age Points from all Holy Sites). When you spread your Religion to cities other than your Holy City, Receive Golden Age points and Food in Holy City equal to the number of Followers of your Religion.
Unlocks Mausoleum National Wonder (+5 Faith, gain Faith when an owned unit is killed in battle. Bonus scales with Era; +5 Faith from all Holy Sites). When a Great Person is expended, gain 5 Faith and Culture for every City following your Religion.
Council of Elders
Unlocks Holy Council National Wonder (+4 Faith, +5 Food; +5 Science from all Holy Sites). When a city adopts your Religion for the first time, gain 4 Science and Production in your Holy City for every City following your Religion.
Unlocks the Celestial Throne National Wonder(+2 Faith, Culture, Food, Science, Gold, and Production; +5 Faith from Holy Sites). Holy City produces +15% of its yields during a Golden Age.
Unlocks Great Altar National Wonder (+5 Faith, +15% Military Unit Production; +5 Production from Holy Sites). Receive Faith and Golden Age points when you conquer a City. Bonus scales with City population and Era.
Unlocks Divine Court National Wonder (+4 Faith, +6 Gold; +5 Gold from all Holy Sites). When you unlock a policy, Receive 3 Faith, Science, and Gold for every follower of your Religion.
Unlocks Grand Ossuary National Wonder (+10 Faith; +5 Culture from all Holy Sites). 'We Love the King Day' boosts the Faith, Culture, and Gold output of a city by 15%.
Way of the Pilgrim
Unlocks Reliquary National Wonder (+4 Faith, +2 Culture, 4 Art/Artifact Slots; +5 Tourism from all Holy Sites). Receive 10 Tourism and Culture when you spread your Religion to foreign cities, scaling with target City size. World Wonders require 1 less unlocked Policy per every 8 Cities following your Religion.
Way of Transcendence
Unlocks Sacred Garden National Wonder (+3 Faith, +5 Culture; +5 Food from all Holy Sites). when you enter a new Era, Holy City gains 25 of every yield for each City following your Religion.
These beliefs provide bonuses for cities following this Religion. You can choose one of these beliefs when founding a Religion, but when the Religion enhances, you may choose another.
All buildings give 'Boosts Pressure of Religious Majority emanating from this city by 25%, and increases this city's Resistance to Conversion by 10%,' unless otherwise stated.
Use Faith to purchase Cathedrals (Reduces Poverty; +2 Gold, +2 Faith; Empty Great Work of Art or Artifact slot; Farms near this City generate +1 Production and +1 Gold).
Use Faith to purchase Pagodas (Reduces Boredom; Empty Great Work of Art or Artifact slot; +2 to all City Yields for every World Religion that has at least one Follower in this City; Doesn't boost religious pressure or resistance to conversion).
Use Faith to purchase Mosques (Reduces Illiteracy; +2 Science, +3 Faith; Empty Great Work of Writing Slot, +20% Culture in the City during Golden Ages).
Use Faith to purchase Churches (Reduces Boredom; +3 Faith; Empty Great Work of Music slot; All Missionaries born in this City can spread Religion three times; +50% Religious Pressure instead of 25%).
Use Faith to purchase Mandirs (Reduces Poverty; +2 Food, +3 Faith; +10% Food in the City; Empty Great Work of Music Slot; Enemy Spies in this City cannot assassinate Great People or disrupt Unit Production).
Use Faith to purchase Synagogues (Reduces Crime; +3 Production, +2 Faith; Empty Great Work of Writing Slot; During 'We Love the King Day', City Science increases by 15%).
Use Faith to purchase Stupas ( Reduces Illiteracy; +3 Faith; +2 Golden Age Points and +4 Tourism once you have researched Architecture).
Use Faith to purchase Orders (Reduces Crime; +2 Faith, +10 City Strength, +50 Hit Points; +15 XP and the 'Morale' promotion for land Military units produced in this city).
Receive 7 to all yields every time a Citizen is born in the City. Bonus scales with Era.
Specialists produce +2 of their normal yield ( Science, Gold, Production, or Culture).
These beliefs provide additional empire-level bonuses that may help you in spreading your Religion. You may choose one of these beliefs when using a Great Prophet to enhance your religion. Enhancing a religion allows Inquisitors to be purchased with Faith in cities where that religion is the majority.
Holy City owner gains +1 Happiness for every two Cities following this religion, and +25% Yields from Friendly/Allied City-States following this religion.
Missionary conversion strength +25%. Holy City gains Science when owned Missionaries spread this Religion to cities of other Religions based on the population of the target City.
Missionaries and Inquisitors cost 30% less Faith; Holy City Owner gains +1 Happiness for every 10 followers of this religion in non-enemy foreign Cities.
Prophets of this Religion 25% stronger, cost 25% less Faith. If the majority Religion, Follower reduction from rival Inquisitors and Prophets halved. +3 to all Holy Site yields.
Religion spreads to cities 20% further away. Pressure to friendly City-States and via owned Trade Routes doubled.
+1 Science and Culture in Holy City for every 10 followers of this Religion in Foreign Cities. Holy City gains 100 Faith each time the owner expends a Great Person. Bonus scales with Era.
Religion spreads 30% faster (60% with Printing Press). Your spies exert religious pressure on the Cities they occupy.
When a city adopts your Religion, Holy City gains 10 Gold for every City following your Religion, scaling with Era. +1 Gold and Faith in Holy city for every 8 followers of this Religion in Foreign Cities.
May spend Faith to purchase land units in Cities. Strategic Resource quantities increase by 3% per following City (up to 50%).
In Vox Populi you need to build your Founder National Wonder or the St. Basil's Cathedral World Wonder to Reform your Religion (you may not Reform twice if you build both).
Followers of your Religion benefit from your Reformation.
Land Units gain +10% Combat Strength vs Land Units in enemy lands, and an additional 10% versus Land Units of players that follow a different Religion. Receive Gold and Culture when you conquer Cities.
Defender of the Faith
Land Units received +15% Combat Strength vs Land Units in own lands, and an additional 15% versus Land Units of players that follow a different Religion. +2 Faith and +3 Culture from all Defensive Buildings.
Faith of the Masses
May build Opera Houses, Museums and Broadcast Towers with Faith. These building produce +5 Culture each.
+10 Science, Culture, Gold, Faith, and Golden Age Points per turn while the Host of the World Congress. Receive 150 of these yields instantly when you pass a Proposal. Bonuses scale with Era.
May build Universities, Public Schools and Research Labs with Faith. These building produce +5 each.
Knowledge Through Devotion
Landmarks and Great Person Improvements produce +3 Faith and +1 culture. Great Works produce +1 Culture
One World, One Religion
Receive 1 additional votes in the World Congress for every 8 City States in the game. Missionaries performing the Spread Religion action erode existing pressure from other religions.
All buildings purchased with Faith provide +3 Tourism each. Hermitage provides +10 Culture and +10 Tourism.
To the Glory of God*
Use Faith to purchase any type of Great Person starting in the Industrial Era. When you expend a Great Person, gain +2 Gold, Science, Culture, and Faith per City following your Religion.
*Purchasing any Great Person with Faith has a cooldown of 5 turns (standard).