You might say the Catholic Church was the glue that held medieval Europe together. Unfortunately, that glue got a kick out of instigating campaigns of terror and death in the name of the big man on the throne in the sky. Executions ordered by popes or carried out in his name by Church authorities were not a civilized affair. Indeed, Vatican execution methods often involved long stretches of humiliation and torture in the build-up to some of the most horrific deaths you can fathom. Heretical thoughts were serious business to Church leaders, so they dealt with them in the most serious ways they could. That seriousness brought about sadism and terror that's still a black mark against the intuition.
Who was persecuted? Jews, Muslims, accused witches, and really anyone who didn’t conform to the Church’s beliefs. Catholic Inquisition executions were often carried out by and at the discretion of friars or other minor religious authorities, acting on behalf of popes or monarchs. So, better to not piss off anyone associated with the Church, lest they elect to slice you to ribbons in the name of God. During this time, you also had executions in Papal States, over which the Vatican held dominion.
Drawn And Quartered: Dragged By Horses And Ripped To Pieces
Burning At The Stake: Business As Usual
Boiled In Oil: More Or Less Self-Explanatory
Water Torture: Forced Ingestion While Choking On Cloth
The Ax: Like A Hot Knife Through Your Neck
Immurement: Walled Up And Left To Die