Throughout Hyrule there are Shrines, many of them hidden and not easily accessible while some only become active once you have completed a Shrine Quest which tends to be in the form of a riddle or puzzle you need to solve, usually inside the shrine itself. Listed below are the various Shrine Quests and what region you can find them.
Dueling Peaks Region
Watch Out for the Flowers - Hila Rao Shrine
The Stolen Heirloom - Lakna Rokee Shrine
Hateno Region
The Crowned Beast - Mezza Lo Shrine
Secret of the Cedars - Tahno O'ah Shrine
The Spring of Wisdom - Jitan Sa'mi Shrine
The Cursed Statue - Kam Urog Shrine
Lake Region
The Serpent's Jaws - Shae Katha Shrine
Guardian Slideshow - Shoqa Tatone Shrine
Faron Region
A Song of Storms - Qukah Nata Shrine
A Fragmented Monument - Kah Yah Shrine
The Three Giant Brothers - Tawa Jinn Shrine
Stranded on Eventide - Korgu Chideh Shrine
Lanayru Region
Master of the Wind - Shai Yota Shrine
The Ceremonial Song - Dagah Keek Shrine
Eldin Region
A Landscape of a Stable - Tah Muhl Shrine
A Brother's Roast - Kayra Mah Shrine
The Gut Check Challenge - Gorae Torr Shrine
Akkala Region
The Spring of Power - Tutsuwa Nima Shrine
The Skull's Eye - Zuna Kai Shrine
Trial of the Labyrinth - Tu Ka'loh Shrine
Into the Vortex - Ritaag Zumo Shrine
Woodland Region
Shrouded Shrine - Ketoh Wawai Shrine
The Lost Pilgrimage - Daag Chokah Shrine
Trial of Second Sight - Kuhn Sidajj Shrine
The Test of Wood - Maag Halan Shrine
Hebra Region
Trial on the Cliff - Qaza Tokki Shrine
The Bird in the Mountain - Mozo Shenno Shrine
Tabantha Region
The Ancient Rito Song - Bareeda Naag Shrine
Recital at Warbler's Nest - Voo Lota Shrine
Ridgeland Region
Trial of Thunder - Toh Yahsa Shrine
Under A Red Moon - Muah Rokee Shrine
The Two Rings - Sheem Dagoze Shrine
Gerudo Region
Cliffside Etchings - Keeha Yoog Shrine
Test of Will - Joloo Nah Shrine
Sign of the Shadow - Sasa Kai Shrine
Wasteland Region
The Eye of the Sandstorm - Dako Tah Shrine
Secret of the Snowy Peaks - Suma Sahma Shrine
The Silent Swordswomen - Kema Zoos Shrine
The Undefeated Champ - Raqa Zunzo Shrine
The Desert Labyrinth - Dila Maag Shrine
The Seven Heroines - Korsh O'hu Shrine
The Perfect Drink - Misae Suma Shrine