Big Priest has grown in popularity ever since the release of Eternal Servitude, Shadow Essence, and Obsidian Statue in the Knights of the Frozen Throne expansion. Since then it has only gotten better utilizing AOE removal and the power of Barnes & Y'Shaarj, Rage Unbound to cheat out big minions.
Kobolds and Catacombs did nothing but improve Big Priest. The addition of Lesser Diamond Spellstone allows for you to resurrect two potentially powerful minions without even upgrading it. Psychic Scream offers an additional way to clear the board in a dire situation.
That brings us to the Standard rotation and The Boomsday Project. The rotation largely killed the original version of the deck. Barnes and Y’Shaarj were both big parts of the list and they are now only available in Wild. However, the deck has had a bit of a resurgence now that Zerek's Cloning Gallery has been added and the list focuses on an OTK combo with Prophet Velen and Malygos.