Giulio Piscitelli / The New York TimesA woman inside the church of the Gesu Nuovo in the historic city center of Naples, Italy, in June. Mystical symbols can be seen carved in the building’s rocky facade, keeping up with the driving forces of life and death that embody the city.

Naples is a city that has seen it all, survived most of it, and, if you have the patience to explore it, will win you over and never let you go.

Naples’ spell can be powerful. More than elegant, restrained Florence or show-offy Rome, with its perfect, ruined beauty, and even more than otherworldly Venice, Naples — earthy, squalid, and slightly menacing — is one of the most romantic cities in the world.

In the years I lived in Rome, whenever I wanted to escape that swampy city, with its oppressive world-weariness, its perennial ability to seduce, but never to surprise, I headed for Naples — and still do — a surefire adrenaline rush, a slap in the face, a semifailed state only an hour south by train.

Sometimes I start at the Café Mexico in Piazza Dante or browse in the secondhand bookstores that line the passageway leading to Piazza Bellini, named for the master of Neapolitan Baroque music, into the ancient heart of the city, “Spaccanapoli,” from the Italian word “spaccare,” to split. It takes its name from what is now Via dei Tribunali, slicing down the middle of the old city first settled by the Greeks. The area is now a warren of dingy, narrow streets, churches, pizzerias and shops selling Naples’ famous Christmas crèche figurines.

Deep in Spaccanapoli lies one of the great wonders of Naples: Caravaggio’s “Seven Acts of Mercy,” surely one of the strangest and most breathtaking paintings in all of art history, a weird chiaroscuro tableau that unites an old man suckling a woman’s breast, a disembodied pair of dirty feet, men in armor struggling in the semidarkness, and high above them a mother and child and two angels, Neapolitan boys really, who cling to each other midfall in a strange and tender embrace.

The unfathomable painting is tucked into the tiny church of San Pio delle Misericordie, inside a palazzo so unassuming and smog-stained that an unwitting visitor could walk past it entirely. In contrast, the city’s other great Caravaggio, “The Flagellation,” at the Capodimonte Museum, is showcased with drama, placed at the end of a suggestively long hallway of galleries. It captures the moment just before Jesus’ tormentors unleash their fateful blows. Every time I’ve visited the Capodimonte, once the hunting lodge of the Bourbon rulers of Naples and now one of the world’s great museums, it is nearly empty, a sign that this city remains an acquired taste, not completely discovered.

The tourists who do come, many of them embarking for only a few hours from cruise ships, tend to flock to Naples’ Archaeological Museum, with its vast rooms of ancient statuary and frescoes from Pompeii as fresh as the day they were painted. (Don’t be surprised if many rooms are closed; the museum says it lacks funding for guards.)

Here, you can see the Secret Cabinet of ancient erotica collected by the aristocratic Farnese family and kept hidden from public view for centuries. Many currents of thought have emerged from Naples over the centuries. Moralism was never one of them.

One perfect spring day a few years ago, some friends and I took the funicular to the former monastery of San Martino, high above the city. From the garden, there is a stunning view of the sweep of the bay — the crumbling, close-packed houses, satellite dishes, the spires of churches with plants sprouting from their cupolas, the industrial port and, in the distance, Vesuvius.

Wandering around San Martino that day, a friend and I came across a room with landscape paintings of the Bay of Naples, the luminous stretch of coastline that first caught the attention of the Greeks in the first century B.C. They made land just up the coast from Naples and named their settlement Cuma after Kymi, the village on the Greek island of Evia, from which they first set sail. (Naples, Neapolis, the new town, came later.) Kymi is also on a bay that rises up a steep hillside. The landscapes, old and new, echo each other. And maybe, I thought to myself that day, the history of the West begins with a handful of Greeks setting sail for farther shores, searching for a place that reminds them of home.

Naples is also a realm of the spirit. In “The Aeneid,” written by a poet from Mantua who felt most at home in Naples, observing the power politics of Rome from afar, Aeneas stops at Cuma on his way back from the Trojan War before founding Rome. There, the Cumean Sybil, so beautifully depicted by Michelangelo in the Sistine Chapel ceiling, advises Aeneas how to descend to the underworld from nearby Lake Avernus to visit his father, but warns of the danger of the journey.

“Offspring / of gods by blood, Trojan Anchises’ son, / The way downward is easy from Avernus … but to retrace your steps to heaven’s air, / There is the trouble, there is the toil,” she says.

Lake Avernus is still here today, now in the semisuburban sprawl outside Naples, surrounded by a NATO outpost.

These days, the grotto of the Sybil — where Ingrid Bergman’s character has a breakdown in “Voyage to Italy,” Roberto Rossellini’s 1955 film — is an ill-marked site, reachable on confusing, local roads, their signs obscured by rushes, in the grim areas that stretch from Naples northward, up the coast, and are the stronghold of the Camorra, the Neapolitan Mafia.

The city’s past sometimes seems to shine brighter than its present. After the quieter years in the 13th and 14th centuries of the Angevin French, who left their mark on some of the city’s most stately medieval architecture, the Bourbons helped transform Naples into the cosmopolitan capital of the vibrant Spanish empire, which it remained for centuries, a hub of commerce and learning. The young Cervantes was stationed here for five years as a marine and the Quartieri Spagnoli, now a bustling working-class neighborhood, was built to house the Spanish troops back in the days of the Kingdom of the Two Sicilies, the period when southern Italy was under Spanish rule. Back then, the Italian south was far richer than the impoverished north. After Italy’s unification in the mid-19th century, living standards and per-capita income in the south plummeted. To this day, many in Naples believe the south was better off before unification.

Naples now has a left-wing mayor, Luigi de Magistris, a former anti-Mafia magistrate, who has tried to solve the city’s persistent garbage crisis, a phenomenon deeply linked to organized crime. The city has never been easy to govern. In 1547, the Neapolitans revolted against the imposition of the Spanish Inquisition. A century later, Neapolitan peasants revolted against their Spanish overlords, furious that they were being impoverished through taxes to pay for Spain’s foreign wars. In 1943, when the Nazis began rounding up Neapolitan men, the furious women of Naples fought back, successfully driving the Nazis out of town, albeit on a killing spree, in a rare mass citizens’ revolt against the German occupation.

In Naples, survival instincts alternate with leaps of faith. The faithful flock to the cathedral to see the miraculous liquefaction of a vial of the blood of San Gennaro, and even St. Thomas Aquinas, the theologian most committed to the demands of the rational, believed that a painting of the crucifixion in the church of San Domenico Maggiore spoke to him. Somehow, in Naples, this all makes sense. Here, the line between the realistic and the supernatural is forever blurred.