One of the big tourist attractions in Zagreb, the capital of Croatia, is a poky and improbable museum without a Bronze Age fragment or a Roman artefact in sight. It is called the Museum of Broken Relationships, a concept that is at once clever, simple and dead cheap.

It comprises a selection of mundane items sent in by the global public to symbolise their own lost loves. Some are touching: a 13-year-old boy’s letter written to a girl he met fleetingly while fleeing Sarajevo under fire in 1992. Some are gloriously vengeful: an axe used to chop up an ex’s furniture. It speaks to us all, of course, because lost love is universal. But it is also place-specific, because the Balkans could be rechristened the Peninsula of Broken Relationships. And Croatia is at its fragile heart.

Like Slovenia next door, Croatia is doing its best to turn its back on the noisy neighbourhood: it joined the EU in 2013, the only new recruit in the past decade. I have heard it argued that its democratic norms did not meet the alleged requirements; that they did at the time but the politicians backslid once safely in; or that Croatia was eligible long before 2013 but unfairly made to wait. This last argument may be the strongest strand, since this country has a powerful sense of victimhood.

I mentioned to someone in Zagreb that my image of Croatia came from the man who might be its most famous son: the 2001 Wimbledon champion Goran Ivaniševic – brilliant, erratic, funny, infuriating, endearing, a bit bonkers. “Oh no, that’s not us,” I was told. “He’s Dalmatian. It’s the Italian influence. They’re all like that there.” It was as if someone had described Geoffrey Boycott as a typical Englishman.

I still think of it as a Tigger of a country. Many of the Croatians I met had an almost Irish gift for the arresting phrase, even in English – so they must be magnificently vivid in Croat. They don’t hold back. As a comment attributed to Bismarck puts it: “The Croats don’t actually know what they want. But they want it NOW.”

They are especially picturesque when discussing the nation’s grievances. One businessman immediately drew my attention to the map. “Most people say Croatia looks like a dragon. But look at it. It’s the Apple logo. You know: someone’s taken a bite out of it.”

Actually, the bite is much bigger than Apple’s; turn the map round and the country looks more like the letter C or U. That bite is Bosnia and the boundary represents the ancient dividing line between Western Christianity – Croatia remains staunchly, or at any rate showily, Catholic – and the Ottoman empire. The country is defined by its strange shape: the plus of its magnificent, long coastline and the minus of its unfeasibly lengthy land borders. When it was part of communist Yugoslavia everything was held together by the force of Tito’s personality, and bits of string. Now Croatia has five separate international borders and boundary squabbles involving all of them. One Croatian said that the country suffered from middle child syndrome, convinced that those above and below them were getting better deals.

Culturally, it is buffeted by cross-currents: here and there are grand buildings fit for grand dukes; notes of waltzes and chocolate torte waft down from Vienna. Gorgeous fresh fish on the coast; sausage and dumplings inland. But there is history, too, and a lot of that is very murky.

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The consensual view of the war of the 1990s, which Croatians call the homeland war, is that the Serbian clique around Slobodan Miloševic was overwhelmingly to blame but that there were also Croatian atrocities (the best short account I know is in Tony Judt’s 2005 masterwork, Postwar). Not all of these are yet fully accounted for, mainly because the Croats – as both victims and victors – have not had the reckoning that comes with defeat.

Yet that is not the only war in living memory. In what Britain still calls “the last war”, Croatia was under direct Nazi rule from the local variant, the Ustaše, led by Ante Pavelic, who may have been second only to Hitler as a genocidal maniac. Again the reckoning was incomplete: even Pavelic died in bed, in Franco-era Spain. Croatia is a place where there are secrets and lies, a sense of unfinished business, of an unconfronted past. A loud country, where some subjects have to be discussed in whispers.

In between there was communism. UK-born Marijana Dworski, who sells Balkan books from rural Wales, has returned regularly to her ancestral home all her life and says the questions she gets haven’t changed since those days: “Where do you live in Lon-don [always pronounced as written]?” “How much do you earn in Lon-don?” “What car do you drive in Lon-don?” The most cherished Western goods in that era were blue jeans, detergent and decent coffee. And to this day, she says, coffee is the gift of choice to take to a hostess, rather than wine or chocolates, though the local coffee shops are ubiquitous and strong enough to keep Starbucks at bay.

What I never did sense in Croatia was the kind of Yugo-nostalgia I encountered in Slovenia (“Where the wind blows softly”, NS, 8 December 2017), and this is backed up by polling data – because Croatia did not have a jolly little war of independence, it had a horrendously bloody war. So its victory remains the central fact of the country’s politics. “There’s this group of half a million people who are recognised as homeland defenders,” says Dejan Jovic, professor of international relations at the University of Zagreb. “They are not one homogeneous body but they are represented by various organisations whose interest is to see the war never ends. They talk as though they are the creators of the state and therefore they are sovereign and the state is not.” Thus they have an effective veto on government policy, of the kind exercised by big money and the NRA in the US and Daily Mail editor Paul Dacre in Britain. Jovic, however, is beginning to sense a change. “My students no longer have a memory even of this war. They’re a new generation. They are also split into several groups. Some are looking to be heroes of the next war and some challenge the heroic narrative completely. But the largest group just repeats the rhetoric as ritual. It’s like communism was for my generation. They learn it in school but they don’t really believe it.”

Eventually this stop-banging-on-about-the-war-dad generation will inherit the country. But it hasn’t happened yet. The conflict in some way touched almost every family in Croatia, including improbable people in improbable ways: the art historian Theo de Canziani was sent, along with other experts, into the battleground frontier town of Vukovar, two weeks after it was liberated, to assess the damage to its heritage. “The place was smoking,” he recalled, “and there was this strange, very sweet smell. It was only later, when my grandmother died and I was with her, that I realised what that smell was.”

As one diplomat observed to me: “You see on the commemorative days that Croatia is not yet ready to move on. They have not got to the point when they can remember the sacrifices on both sides. There’s a quick mention of Serb deaths in the politicians’ text but then they’re into nationalist celebrations and even chanting Ustaše slogans.” And after the war criminal Slobodan Praljak’s suicide in court in November (an act of what seemed to me very Croatian theatricality), there was an unseemly degree of sympathy.

The war did achieve, more by chance than judgement, a nationalist objective that sets Croatia apart from most developed nation states. It has gone from being multi-ethnic, multicultural and multi-religious to more mono-ethnic, monocultural and mono-religious. Croats rushed back from neighbouring countries to replace the minorities who fled the other way. Not merely did Croatia end up as an independent state and a member of both Nato and the EU, its minority population went down from 22 per cent to below 8 per cent. “This did create a sense of stability,” explained Bojan Aleksov, senior lecturer in Balkan history at University College London. “But externally it brought lots of troubles, particularly Croatia’s bad relations with its neighbours.”

That homogeneity helps a lot of mould fester behind the democratic facade. “We have a politicised civil service and judiciary and high levels of patronage,” a political analyst told me. “They always talk of reform. It goes down well in Brussels. It goes down well locally. But nothing ever happens. Court cases last five, ten, 20, 30 years even. A 30-year divorce case? Can you imagine?”

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Homogeneous or not, there are (over-simplifying somewhat) three very different Croatias. The Croatia the world knows is its frontier with the kindly and beguiling Adriatic – a thousand islands, islets and reefs, 3,600 miles of coast in all. Here the communist-era blocks of flats are now being matched by the jerry-building of the new capitalism, and the country’s highly successful tourist industry.

Aleksov gives the credit to Islamic State. “No one wants to go to Egypt, to Turkey, to Tunisia. So they go to Croatia. We go every year and notice some terrible new tourist development and tell people no one’s going to come to Croatia because these places are so dreadful. And they tell us that every year it’s fuller. Fifteen per cent increases. So what can you say?” (If your hotel collapses, don’t even think of suing. Not in Croatia.) As well as the shoddy buildings, there are smart new ones too, built dubiously without obvious regard to the technicalities of ownership, never mind planning regulations. There are people here with whom one does not argue.

Inland, there is Zagreb, a lively and attractive city, and the prosperous region nearby. But I took a pre-dawn train east from Zagreb into Slavonia – not to be confused with Slovenia, Slovakia or indeed Snowdonia. “Pancake-flat, river-rich Slavonia,” the Lonely Planet guide’s very short section on the region begins, “is all but untouched by tourism…” It then devotes the next few pages pretty much to explaining why it’s likely to stay that way.

The entry does not even mention Slavonski Brod, the second-largest town in the region, though it is set on the broad River Sava looking across to Bosnia, and is both historic and attractive – provided the wind is not blowing smoke from the Bosnian oil refinery their way. This was not one of the places the world half-heard of on the news while quarter-understanding the hell the Yugoslavs were inflicting on each other in the 1990s. But in the summer of 1992 it was bombed on a daily basis as the Serbs tried to breach the bridge over the Sava.

Twenty-eight children were killed there – more, I was told, than anywhere else in Croatia – a story depicted on accusatory Belfast-style murals facing the river. And in a playground nearby there is the official monument to all the Croatian children who died: a 15ft-high metal jigsaw with a couple of pieces missing. It was unveiled last year and is the most affecting war memorial I have seen.

But Slavonski Brod is still losing its children, not as tragically but perhaps almost as finally. There is a strong industrial tradition here and the local college still turns out kids ready for the workplace, in metal processing especially. They find jobs all right, just not here – but across the EU’s free-labour market, in Germany, Austria and (the UK having pulled up the drawbridge by the time Croatia joined) Ireland.

The deputy mayor, Hrvoje Andric, speaks at the graduation ceremonies: “These young people are a strategic resource of the Croatian republic,” he told me. “I tell them, ‘Each one of you is worth more than a freshwater spring or a beach on the coast.’ It’s hard to look at these people and think that at least half of them will be gone in months. We are doing our best to improve the town. But central government has no idea how to stop this happening. We have to have some return value on these people or it’s not fair.”

The council’s development officer, Dejan Vuksanovic, talks proudly about the innovation incubator that is helping tech firms get started and provide jobs at home. “But why wouldn’t your brightest kids go to Germany, where they can earn three times the money?” I asked. “That’s the problem,” he replied sadly. The irony is that if one of these companies does take off, it will have to recruit from the poorer countries of the Balkans, bringing back the very minorities to whom Croatia has just said good riddance.

In the second half of the 20th century Slavonski Brod’s population trebled to a peak of 64,000. Now it is falling sharply. In rural Slavonia the problem is even worse: whole villages deserted, fields untilled. And there is a new crisis: the collapse last year of supermarket chain Agrokor, a company that bought up pretty much every major food and retail business in Croatia in a way that made Enron look rock-solid. Its founder, Ivica Todoric, was last heard of in that well-known offshore bolt-hole, London, where he was arrested on a European warrant and bailed in November. A fair few high-ups in Zagreb will be hoping he stays there.

Free movement of labour must sound great at BMW HQ in Munich, less so here. This does not mean Croatia is jealous of Britain as we head to the EU’s exit. Indeed, the most withering comment on Brexit I’ve ever heard came from the art historian de Canziani: “You know, the Pekinese was a big dog once, but the size was bred out of it. So when it sees another dog it thinks it’s still big and tries to bark. But it can’t. It can only yap.” Ah, these Croatians: they could be wordsmiths to the world.