I assume you’re referring to the Golden Age of Piracy, since worldwide piracy never really ended, only changed. The Golden Age lasted approximately from the mid-1600s to about the 1720s, during which time piracy was so common that many of its most prominent figures became celebrities, and still are to some degree—Blackbeard, Calico Jack, Mary Read, Anne Bonny, Sam Bellamy...

The decline of piracy is closely linked to factors of its rise, namely, a cocktail of European politics, colonial wealth, and geographic isolation. There was no other place and time in world history like the Caribbean in the mid-seventeenth to mid-eighteenth centuries. At the start of the period, practically the entire New World was under the complete authority of the Spanish crown, to whom it had been granted after the Treaty of Tordesillas in 1494. Since then, the Spanish had conquered two great indigenous empires and pressed the populations into service extracting precious metals like silver at the Incan mine at Potosi, and transporting the bullion back across the Atlantic and Pacific oceans to enrich the empire in hulking treasure galleons. Because their primary goal was maximum extraction at the lowest possible cost, and because they were essentially the only game in town, the Spanish didn’t really bother to fortify the towns that punctuated the overland routes or patrol the thousands of islands and keys in the Caribbean. On top of that, the galleons sailing in and and out of these ports followed established routes on regular schedules. The routes were so well-traveled by the Spanish that it gave rise to the term the Spanish Main. These factors--enormous wealth traveling largely unprotected over great distances across isolated routes--made the Caribbean ideal hunting grounds.

As Spain started to flaunt this new wealth (and by “flaunt” I should probably say “hemorrhage,” because they were also basically constantly at war with the other European powers), the French and English governments wanted to deal a blow to their rival and also maybe get a piece of the action. The respective crowns begin issuing the infamous “letters of marque” to enterprising sailors authorizing them to attack merchant and navy ships sailing under the banner of hostile nations with the condition that a portion of captured plunder be shared with the authorizing country. These privateers, as they were known, were basically state-sponsored pirates, and included the likes of William Kidd (who mostly operated in the Indian Ocean) and, especially, Woodes Rogers (remember that name) and Henry Morgan. As a young man, Morgan was part of the British expedition that captured Jamaica, which provided a foothold for the privateers smack in the middle of the Caribbean, within striking distance of the primary treasure routes. Over the course of his career, Morgan lead several successful raids on Spanish treasure ports in Central America, in particular Portobelo in Panama. His exploits earned him a lieutenant-governorship in Jamaica. During his tenure, the capital city in Jamaica, Port Royal, played host to privateers and pirates alike, blurring the line between licit and illicit sea raids in the Caribbean.

All during this time, the Spanish complained of the privateers, not only because they were picking Spanish pockets but, operating in such a remote part of the world with essentially no oversight by their authorizing countries, things turned dark. One French privateer named L’Olonnais, for example, was known for his cruelty, and at least once sliced a captured Spaniard’s stomach, nailed his guts to the deck of his ship, and forced him to dance until he eviscerated himself. As barbaric as the time was, all “civilized” authorities generally agreed on certain rules of military engagement, and the privateers existed wholly outside those rules. The French and British usually just paid lip service to the Spanish, though, making nominal concessions. Morgan, for example, was ordered back to London for his raid on Portobelo, during which his men committed atrocities in the course of razing the town, but there he caroused and schmoozed his way through a sham hearing before returning to the West Indies with, of all things, his royal appointment in Jamaica.

This was the state of things until about the end of the War of the Spanish Succession in the early eighteenth century, when the major European powers generally agreed to conclude hostilities with one another. As a result, their governments stopped issuing letters of marque and started treating those privateers as true pirates, men outside the law. By this point, though, piracy had become a fact of life in the Caribbean, and the privateers who had made a living—as well as untold swarms of navy sailors who had fought in the war but were now unemployed—were not about to give it up.

In 1694, the main pirate haunt of Port Royal had been cast into the sea by an earthquake, so the pirates had unofficially chosen a new place to retreat, refit, and spend the fruits of their ill-gotten gains: Nassau, on New Providence Island in the Bahamas. The pirates who holed up here went by the name of the Brethren of the Coast, a loose affiliation of pirates including many of the names I mentioned at the top. If you’ve ever heard of a pirate republic, this was it.

At this point, Britain had transitioned from living off the table scraps of the Spanish Empire to establishing its own profitable colonies in the Americas, not just in the Caribbean but on the eastern coast of North America. The lucrative trading network they had established was now being threatened by the pirates, who were by now regularly raiding merchant ships and towns in the Caribbean as well as up and down the Eastern Seaboard as far north as Maine and Newfoundland. The men the crown had profited from were now cutting into their own profits, and so it was now in their interest to see it ended. At first they offered pardons to those who agreed to give up the piratical life, and this certainly cut into the buccaneers' ranks. But again, the reality of being a sailor in the eighteenth century made living at the edge of civilization preferable: what little legal work there was to go around either on merchant ships or in the navy was hard, bad paying, and demeaning. So many pirates, including Calico Jack Rackham and Charles Vane, would take pardons to escape punishment on capture only to turn around and run off back to the pirate haven in Nassau.

When the pardons proved ineffective to quash piracy, the British looked to cut off the insurrection at its head, turning to one man who had a fair bit of experience in the privateering life: Captain Woodes Rogers. Rodgers was one of a few privateers who considered himself to be a patriot, refusing to attack any ship belonging to Britain or its allies. The British admiralty selected Rodgers to lead a convoy of ships to retake Nassau from the pirates by any means. A few accepted pardons, including Captain Benjamin Hornigold, who turned to pirate hunting himself. But a few pirates, including Jack Rackham, Read, Bonny, Blackbeard, and Sam Bellamy, the last two powerful captains in command of fleets in their own right, slipped off into open waters. Their refusal to accept the pardons made them enemies of the crown. Nassau, the last refuge of pirates in the Caribbean, fell to civilization.

From then on, the pirates lived hunted lives. Scattered and without the support of a base of operations, they each met their ends. In 1717, Sam Bellamy and his ship the Whydah wrecked in a storm off the coast of Massachusetts. In 1718, Blackbeard was cruising off the coast of his old hunting grounds in Ocracoke, North Carolina, when he was attacked by navy vessels under the command of Lieutenant Robert Maynard. Blackbeard died in the fighting, and his crew surrendered. Maynard hung the old pirate’s head by the bowsprit of his ship as a prize. In 1720, Rackham, Bonny, and Read were captured off the coast of Jamaica after their crews captured a prize and got roaring drunk. Rackham was tried and executed, while Read and Bonny were convicted, but "plead their bellies" and were offered a stay because they were pregnant. Read died from illness while in prison, and Bonny faded into obscurity.

The pirates existed only in a brief window of time when the circumstances of history were right. It’s ironic that the same politics of empire that fueled their rise eventually spelled their demise, bolstered by their governments until it was politically or commercially inconvenient, then disowned and hunted across an open ocean that became less open over time.

Sources: Empire of Blue Water, Stephen Talty Pirate Hunter of the Caribbean, David Cordingly The Republic of Pirates, Colin Woodard Under the Black Flag, David Cordingly

Edit: Thanks for the gold! Hopefully I can find a way down to the Bahamas to spend it... Cheers. Also, a few edits to the original (because Captain Morgan did not raid a portobello mushroom but the Spanish treasure port of Portobelo).

I've written a post here (this and this get into some of the economics of it) attempting to explain how the so called "Golden Age of Piracy" ended in the Caribbean in the early 18th century and Caribbean piracy virtually ceased after that for the rest of the 18th century. However, Caribbean piracy did once again see a resurgence in the early 19th century from about the 1810s to early 1830s following the end of the Napoleonic Wars and various Latin American wars of independence, but this was never quite as big and grandiose it was in the early 18th century following the Spanish War of Succession. This wave of piracy came to an end for similar reasons as it had a century before when government navies aggressively hunted them down but I don't know as much about that. So I hope my link at least partially answers this question.

This is my first time responding, but also the first time I have seen a topic I am knowledgeable about. I hope this gives some insight into the situation, and please feel free to ask questions!

The golden age of piracy occurred around 1690-1760. This period of time made the West Indies (the Caribbean) the most profitable yet still distant from Europe. Spain controlled Central America, France had the Louisiana Area (think Louisiana Purchase), Denmark was in South America as was Portugal. England control the eastern seaboard and some of the various Caribbean islands (Herman Moll Map of Indies).

During this period land itself meant wealth, so every portion of land that could be seized and held was of importance. Add into this all the unsullied forests and you have a treasure trove sitting across the ocean that any county in Europe would kill for, literally (Hattendorf Maritime history Vol 1&2).

The knowledge of reaching the Indies was mostly just a sea captain using the currents and “dead reckoning” to cross the Atlantic and try to get to the Caribbean to trade the lumber, slaves, tools, colony provision etc. The more that the countries began to invest into these colonies and the more they received home, the greater value of these investments. This obviously led to the need to protect them better from Pirates, or privateers of other nations.

The English crown offered a bounty in 1714 to the person would go devise an accurate sea clock to keep the time while at sea, and thus make traveling across the Atlantic safer, and swifter for naval ships. When this finally did occur (though not to the satisfaction of the bounty’s keeper yet) Large naval forces crossed the sea for more frequently and were able to begin enforcing the Laws of the sea. (Sobel’s Longitude)

With all the extra security, increase military presence, and the ability to simply execute pirates granted by the Admiralty courts, Piracy was dealt with quickly and efficiently. Many of the more famous pirates were captured and executed by the 1720s’.

I strongly recommend A General History of Pyrates written in 1724 (found free here: https://www.gutenberg.org/files/40580/40580-h/40580-h.htm)