It's all 'Rock Steady!' in Gibraltar's thriving tourism scene. Or maybe not. As the Rock introduces radical tax changes from January as part of its transformation from an offshore tax haven into a conventional financial centre, tourism is bound to feel the effect.

"We want continuous growth in tourism," says Ernest Britto, Gibraltar's Minister of Tourism since 2007.

Unlike the majority of the sunny Mediterranean's modern beach-dominated attractions, Gibraltar's tourist lure is more focused on history. Many, many layers of history. From the Second World War, back to Neanderthal man, who seems to have chosen Gibraltar as his last known crash-pad.

Gibraltar's multiple histories, says Professor Clive Finlayson of the Gibraltar Museum, "means you've got the Neanderthals, the Phoenicians, the Muslims coming in, the Spanish, the Christians coming in, the turmoil of the British period...and you see them when you excavate any part in the town. The Rock is like a time machine."

You know you're not in a typical Mediterranean resort as soon as you arrive by plane or car. The Gibraltar airport runway, the smallest in the world and built during the Second World War, crosses the main road into the town. Visitors are dumbfounded when traffic is stopped to allow planes to take off and land.

Once you are on Main Street, Gibraltar's biggest thoroughfare and shopping area – all VAT free, another lure for tourists to the Rock – you note a more recent history. The pound sterling is the currency and cops are English Bobbies with the characteristic helmet and uniform, speaking Spanish!

All around, everything seems to still be in the 1990s, 1980s, 1970s... This is Britain as you remember it maybe in your youth. Yet it's not really British, it's not Spanish, although the feeling is of a "home from home", a mini UK in the sun. How will the embracing of a serious European-style financial system affect this? It's maybe time for a pint in one of the southern-most British pubs in Europe...

Gibraltar was an important operations base in the Second World War, and much of the Rock's 50 kilometres of tunnel – more than its surface road – were built during the war.

General Dwight Eisenhower in November 1942 directed the Allied invasion of North Africa known as Operation Torch from a former NATO regional headquarters deep inside the Rock. The UK Ministry of Defence used the same secure area until two years ago, when it was taken over by a data storage company.

Part of the Second World War tunnels includes O'Hara's Battery, a once decrepit site that has been renovated into a top attraction. O'Hara's Battery is the highest point of Gibraltar at 426 metres (1400ft approx).

The Governor believed if such a tower was built it would enable the garrison to see Cadiz and any ships heading towards Gibraltar. After it was built and his theory was dashed, it became known as O'Hara's Folly. The Second World War battery is still on MoD property and a locked gate prevents anyone getting to it. It is the final destination on the trek along the Mediterranean steps before the walk back downhill past St Michael's cave and on to the Ape Den.

Another worthwhile historical visit is to the Great Siege Tunnels, from where in 1789 the forerunners of the Royal Engineers built tunnel systems to position guns to keep back the enemy.

St Michael's Cave, regarded as one of the 10 best caves in the world, has amazing stalagmites and stalactites, and was inhabited for a while by Neanderthals as well as Neolithic man.

The Rock's Upper and Middle galleries are part of the honeycombed inside of the limestone Rock. A tour of the Upper and Middle galleries takes in thousands of years of Rock history, and this includes the notorious Barbary Ape Den, where Europe's only free roaming primates hang out when they're not looking for food from human visitors who have come to take their photos. The Ape Den has recently been facilitated with new flooring and steps – but watch out for leftover fruit and other ape food that is lying often half-rotten on the ground.

The Moorish Castle is famous for its resistance to past sieges. Construction began in the 8th century, but its completion date is unknown. The Moorish Castle played a major role in the Arab conquest of the Iberian Peninsula, overrun in just two years (apart from the northern region of Asturias). This invasion led to Arab domination of a part of Europe for nearly eight centuries, essentially from 711 to 1492, although the Spanish reoccupied Gibraltar in 1462.

Back to the present, other key attractions include dolphin safaris and wreck diving. The Bay of Gibraltar is home to several species of dolphin and many companies organise dolphin safaris.

Deep below the Rock's Upper gallery is another wonderful Gibraltar universe – the underwater world of 30 shipwrecks from many wars, reefs and pinnacles. Seven Sisters is a series of rocky pinnacles just offshore, which offer a stunning array of corals and 165 different species of invertebrate.

And if so much history and sea activity isn't your thing, you can always take a day-trip to Spain or Morocco.