There have been two key drivers: the accession of eight central European countries into the EU just over a year ago - Poland, Hungary, the Czech Republic, Lithuania, Slovenia, Estonia, Latvia and Slovakia - and a strong economic recovery in Russia.
There are two main funds that specialise in this region available to private investors: the £340m Jupiter Emerging European Opportunities, which celebrated its third anniversary last month; and the £28m Credit Suisse European Frontiers.
A £1,000 investment in the Jupiter fund three years ago (to 17 October) would now be worth £3,154, after charges and basic-rate tax, according to figures from ratings agency Standard & Poor's. And the Credit Suisse fund would have turned a £1,000 investment into £3,041. The value of both is up by around 50 per cent in the past year alone.
Ingrid Kukuljan, co-manager of the Jupiter fund with Elena Shaftan, says the EU accession is important as it means that Central Europe is far less risky than in the past. Legislation and regulations have been harmonised with those of the EU, leading to better corporate governance.
Mike Lenhoff, chief strategist and head of research at stockbroker Brewin Dolphin, which has recently added the Jupiter fund to its buy list, says these countries aspire to the living standards of the West, which is driving consumption. Meanwhile, their cheap and skilled workforces are helping to attract the overseas investment that will set them on the long-term path to prosperity. Additionally, low taxes and higher spending are resulting in more stable economies.
Gavin Haynes, a portfolio manager at Whitechurch Securities, says economic growth in converging Europe is far outpacing that of the eurozone.
The flipside, though, is that investments are not as cheap as they used to be. "We have already seen a very strong re-rating in the valuations of shares," he says. "For example, the Hungarian and Czech stock markets currently trade at price- earnings ratios [a measure of company valuations] of over 20 times, compared to 10 times three years ago."
Russia, of course, remains outside the EU orbit, and political concerns have dominated this market over the past few years.
But Ms Shaftan says the economic backdrop has improved. After reaping the benefits of a high oil price and responsible government policies, the country has current account and budget surpluses.
Russia dominates most emerging Europe funds, says Stephen Marriott at independent financial adviser (IFA) Bestinvest. It currently accounts for 47 per cent of the Jupiter fund, for example. But he says investors need to remember that oil is the backbone of the Russian economy - so price movements in the black stuff will have a big influence on these funds.
"When investing in emerging Europe funds," he adds, "be aware of the weightings towards specific countries and sectors."
But Mark Dampier at IFA Hargreaves Lansdown says the opportunities in Russia are not restricted to oil.
"Mortgage lending has not even started in the country, so the growth potential is enormous," he says. "Mobile penetration in Russia is also a low 70 per cent, and in other republics of the former Soviet Union it is still below 50 per cent. This compares to above 100 per cent penetration in most of Western Europe, so there is plenty of room for catch-up."
A marked improvement in Russia's relationship with the West has also furthered the outlook for its exporting companies.
But Mr Haynes at White-church warns that despite these positive factors, Russia carries risks. "Areas such as banking still require reform, while scandals like the one at [oil giant] Yukos highlight the need for better corporate governance."
The consensus among investment specialists is that funds backing these areas can continue to deliver strong growth - though Mr Haynes feels the "easy money" has probably already been made. It is unrealistic, he explains, to expect such strong returns to be repeated in the short term.
That said, he believes there is still good reason to include the funds within a diversified portfolio. "These markets are suitable for investors seeking long-term growth opportunities [of five to 10 years or more]."
Philippa Gee at IFA Torquil Clark points out that if you already have a managed fund, it is likely you will have an allocation in this area. "For someone with a well-diversified portfolio, 5 per cent is a sensible weighting."
Mr Dampier at Hargreaves Lansdown agrees, but says investors should be prepared for a bumpy ride, because these markets can be extremely volatile.Reuse content