Twelfth Night (1599 or later) is the last of Shakespeare's happy comedies. After that, while he was writing his great tragedies, Shakespeare wrote problem comedies. Here's the probable sequence:

c. 1600 - c. 1607
Troilus and Cressida
All's Well that Ends Well
Hamlet
Measure for Measure
Othello
King Lear
Macbeth
Antony and Cleopatra
Timon of Athens
Coriolanus

c. 1607 - c. 1613
Pericles
Cymbeline
The Winter's Tale
The Tempest
Henry VIII

Common Characteristics:
1. They cover a lot of time and space.
--In Pericles, at the beginning of the play Pericles is a young unmarried man; by the end of the play his daughter Marina is an adult.
--Pericles is Prince (ruler) of Tyre, sails to Antioch, where he discovers the terrible secret; returns to Tyre, but then flees to Tarsus. Later he is shipwrecked in Pentopolis, in modern day Libya. Wins a tournament and so his wife, Thaisa; they head back to Tyre, but she apparently dies in childbirth There's a storm, her casket is put overboard & washes ashore at Ephesus. Pericles leaves his daughter to be raised by a couple in Tarsus, but pirates kidnap Marina and then sell her to a brothel in Mytilene
--In Cymbeline the back story goes back 20 years; Cymbeline is the British King, but the Roman army has an important role.
--In The Winter's Tale there are two locales, Sicily and Bohemia (present-day Czech Republic); there is also a 16-year gap in the middle of the play, to allow for the fact that Perdita, not born when the play opens, becomes a beautiful young maiden.
The Tempest

2. They all have strong elements of the marvellous.
--In Pericles a riddle tells Pericles that there is an incestuous relationship between the King of Antioch and his daughter; and storms are an essential part of the plot.
--In Cymbeline there is the following stage direction:

JUPITER descends in thunder and lightning, sitting upon an eagle; he throws a thunderbolt. The Ghosts fall on their knees.

3. They conclude with the hero's recovery of...
--In Pericles, his wife and daughter.
--In Cymbeline, Posthumous Leonates recovers his wife, after ordering her murder, and King Cymbeline recovers his daughter. It's the same woman, Imogen
--In The Winter's Tale Leontes, King of Sicily, recovers both his wife, Hermione, and his daughter (long) after ordering the death of both.
--In The Tempest . . .

In its spectacular effects, The Tempest may have been influenced by the Masque, many of which were written by Shakespeare's friend, Ben Jonson. -- About the Masque of Beauty, script by Ben Jonson, design by Ingio Jones: "The total cost of producing the masque was £4000.[3] The House of Stuart was running an annual budget deficit of £140,000 in this era;[4] the cost of the masque represented about 3% of the annual deficit, an enormous sum to spend on a single event. Our current national deficit is in the neighborhood of 15 Trillion USD. Do the Math. -- About the stage effects: See the Wikipedia Page on The Masque of Blackness -- The show presented to Ferdinand and Miranda is a masque minus the scenery and the dancing.

In their content, the Romances are seen to be similar to Medieval Romances, hence their name.

Also, they may have been influenced by Shakespeare's age. He was 47. Kent, in King Lear, is 48.

The Tempest was certainly influenced by the discovery of the New World, and the reaction to it, particularly in Montaigne's essay Of Cannibals

• Act 2, Scene 1: Gonzalo's Utopia
• First entrance of Caliban