Here are some one liners...
Anti-inoculation Bomb Throwers Fizzle Out -- Small pox has infected half of Boston. A few people are shouting for inoculations but others object. A grenade is tossed into the living room of Cotton Mather, who recently had his son inoculated.
The Modern Russian Empire Begins -- Peter the Great becomes Emperor Peter as Russia steps up to Empire status.
The Popes Are Reforming the Church Slowly -- The New Pope will implement reforms in the Church and when he dies his successor will implement more. Little by little it is getting done.
Anti-inoculation Bomb Throwers Fizzle OutDespite quarantine efforts, almost half of Boston is infected with small pox. Red flags fly from doors where the deadly disease has struck. Reverend Cotton Mather is been campaigning for small pox inoculations. He submits his own son, Samuel, to the experiment along with 248 volunteers. Many people think he is simply spreading the disease further. James Franklin, the elder brother of Ben Franklin and publisher of the New England Courant, is vigorously opposing inoculation. The people are in a panic. Tempers flare and someone has lobbed a grenade into Cotton Mather's home. It rolls under Mather's chair. The fuse fizzles and dies. It is a dud. At the end of the epidemic, 844 Bostonians are laid to rest. Samuel Mather lives. Out of the inoculated, only 6 die, but very few have learned this lesson... not even Benjamin Franklin who will watch his son, William, die of small pox a few years later. In 1759, Benjamin Franklin will have a pamphlet printed to promote the inoculation of children.     
The Modern Russian Empire BeginsThe Great Northern War has ended better than expected for Russia. With the recent treaty, Tsar Peter the 1st (otherwise known as Peter the Great) gives up claim to most of Finland except around the capital of Saint Petersburg and he picks up Estonia, Livonia, Ingria. He also pays 2 million thalers to Sweden to call it even. Russia has been expanding the equivalent of a Netherlands every year. (There is even a Russian village in Alaska.) This treaty marks the transition point for Russia into an Empire that will live on until 1917. Emperor Peter the Great has managed to drag Russia into the modern era, and he is making the rest of Europe nervous. They have enough trouble managing with a Holy Roman Emperor. Most of them don't want a second Emperor to deal with.  
The Popes Are Reforming the Church SlowlyPope Innocent the 13th bans the practice of nepotism... that is... handing off cushy jobs or land grants to relatives. He also reduces spending. He will hold the office for a few years and when he dies he will be succeeded by a man of few words... The Servant of God, Pope Benedict the 13th. He will abolish the lottery in Rome, and force a reduction in the lavish lifestyles in Rome. Benedict will also lift the ban on smoking.  
This Year in Wikipedia
Year 1721, Wikipedia.