Short answers, pulled from the story.
The immediate cause was unpaid Imperial troops who mutinied and forced Duke Charles III of Bourbon to lead them on Rome. Charles V had dispatched the army to pressure Pope Clement VII diplomatically, not to sack the city. Once the soldiers mutinied, no commander could hold them back.
An estimated 6,000 to 12,000 people were killed in the Sack of Rome, with approximately 2,000 bodies reportedly thrown into the Tiber River. The city's population fell from over 55,000 before the attack to just 10,000 afterward, due to killings, plague, famine, and flight.
Pope Clement VII fled through the Passetto di Borgo, a secure elevated passage connecting the Vatican to Castel Sant'Angelo, where he remained as an effective prisoner. He surrendered on the 6th of June 1527, agreeing to pay a ransom of 400,000 ducati and to cede several territories to the Holy Roman Empire.
Of 189 Papal Swiss Guards stationed at the Vatican, only 42 survived the Sack of Rome. Led by Hercules Goldli, this group held off the Habsburg pursuers long enough for Clement VII to escape through the Passetto di Borgo. In commemoration, new Swiss Guard recruits are sworn in on the 6th of May every year.
The Sack of Rome indirectly triggered the English Reformation. Charles V's aunt was Catherine of Aragon, wife of King Henry VIII of England. After the sack, a weakened Clement VII complied with Charles's demand to deny Henry's annulment request, and Henry VIII broke with Rome.
The Sack of Rome permanently deepened the divide between Catholics and Protestants. After the sack, Clement VII agreed to convene a Church Council; his successor Pope Paul III opened the Council of Trent in 1545. By then the window for reconciliation had closed, and under Charles V and his son Philip II of Spain the Inquisition became pervasive throughout the Catholic world.