For many Global 100 firms, the past year has exposed how complex and risk-laden managing an international law firm has become.

Firm leaders have been forced to manage against a downturn in commodity markets, turmoil in foreign exchange markets and slow growth in many of the world's key economies. Moreover, the UK's vote to leave the European Union (EU) has put at risk decades' worth of investment in London by global firms.

The net effect is that many firm leaders are rethinking the conventional wisdom that has guided their international expansion. In Europe, global firms are beginning to look less London-centric. In China, firms are taking divergent paths. Some are exiting, while others are investing in local expertise.

What is clear is that firms are not responding to trouble in the global economy by backing away. Instead, they are embracing a more nuanced, less hub-and-spoke approach that forces them to engage with a wider range of markets. This is true in developed markets such as Europe and in emerging markets including Africa, Latin America and southeast Asia. Here is a snapshot of legal markets that global firms are actively rethinking.

London

US firms have invested heavily in London during the past two decades. UK firms have used the city as a launching pad for their global expansion. All of that is at risk now that the UK has voted to leave the EU. While a worst-case scenario – the end of London as Europe's financial headquarters – appears unlikely, many global firms are evaluating and preparing for other scenarios.

London's importance to global firms should not be underestimated. US firms have more than 6,000 lawyers working in the city. That's more than three times higher than any other metropolitan area outside the US. It represents nearly half of US firms' lawyers in Europe and more than a quarter of their non-US lawyers throughout the world. London remains one of the most profitable international markets for US firms, thanks to strong demand for finance and M&A work.

For UK firms, the stakes may be even higher. London firms haven't penetrated New York the same way that US firms have infiltrated London and this has left UK firms more concentrated in their home market and more exposed to Brexit-related risks.

Global firms' immediate response to Brexit has been to ensure that their UK-based lawyers can continue practicing in European courts. To that end, many firms are registering their UK-qualified lawyers in Ireland, with the number of English lawyers applying for Irish certification jumping by more than 300% so far this year.

The next phase of the Brexit saga will be absorbing the short-term financial fallout. The good news is that many firms have reported an uptick in client inquiries precisely because of Brexit worries, with an expected increase in regulatory and contracts work. More worrying is a potential downturn in work on high value transactions. Market turmoil often creates a slowdown in transactions and signs already point to declines in M&A and IPO activity in Europe. If that market does not rebound, law firms could see significant impacts on their financial performance in the coming year.

The longer-term worry is that London's status as Europe's premier financial centre might wane. Citigroup, Goldman Sachs, JPMorgan Chase and other major financial institutions have said the vote to leave the EU would cause them to reconsider their presence in London. If those companies shifted work to mainland Europe, global law firms would almost certainly follow. While that outcome is not certain, it remains a major medium-term risk for global law firms, which have placed long-term bets on London.

Continental Europe

Continental European markets are likely to become more important for global law firms during the next few years. If London's role as the financial centre of Europe diminishes as a result of Brexit, the region's other cities have much to gain. Even if that outcome does not materialise, the rationale for global firms to have a robust continental presence is getting stronger as the legal and regulatory market coheres.

Two European markets look particularly attractive to global firms: Brussels (right) and Germany. As the political capital of the EU, Brussels is increasingly acting as the regulatory and legal headquarters of the continent. That shift has drawn in global law firms, particularly US firms advising multinationals on EU regulatory matters. At present, more than 50 global law firms have a Brussels office, with a combined total of more than 1,000 lawyers.

As the largest economy in the EU, Germany has the most to gain from Brexit worries and from the increasing cohesion of the single market. If London wanes, Frankfurt and Munich are natural next stops for global financial institutions and global law firms. Those cities, as well as Berlin, have risen in prominence as Germany has emerged as a key political and economic leader in Europe.

The intense activity in the lateral partner market in Germany during the past several years is a clear indication that global law firms are responding to that country's increasing importance. Last year was a banner year for lateral partner hires in Germany, and 2016 is on pace to match it. Clifford Chance, Dentons, Goodwin Procter and Mayer Brown are just a few of the firms that have poached partners this year. The focus appears to be on corporate practices, though firms are also hiring in intellectual property, finance and other practice areas.

China

The long-term promise of the world's largest economy is clear, but the competitive dynamics within China's legal market have made it difficult for many global law firms. Rules prohibit foreign firms from practicing Chinese law. And global firms face competition from peers and domestic firms. Those factors threaten profit margins for many global firms in China.

Despite the difficulties, firms appear unwilling to exit China. Many believed that decisions by Chadbourne & Parke and Fried Frank Harris Shriver & Jacobson to close their Chinese offices in 2015 were a harbinger, but few firms have followed suit. Many firms still believe in the long-term promise of the Chinese market; inbound and outbound investment remains strong and many firms believe their global brands give them a natural advantage in winning this work. Also, many firms fear that exiting China will hurt their prospects elsewhere. Multinational clients report that they prefer firms with a global presence. A lack of a Chinese offering, firms fear, will leave a big hole in their international network.

While some firms have responded to the situation by remaining as lean as possible, others are trying to develop a stronger local offering to increase their competitiveness. The most notable example is Dentons' merger with Dacheng. The merger provides Dentons with more than 40 local offices and 3,000 local lawyers. Other global firms are pursuing similar, if less dramatic, approaches. Earlier this year, Linklaters spun off its Shanghai office. The firm's Chinese lawyers in Shanghai will create their own firm allied with Linklaters, allowing the UK firm to effectively offer local services. Such strategies may become more common as firms seek to differentiate themselves and compete more directly with local firms.

India

Liberalisation of the Indian legal market has been reportedly near for a decade – and this time it might be serious.

Strict laws now limit the range of activities that foreign firms can perform. Those laws have effectively barred global law firms from opening local offices or practicing local Indian law. Firms have tried to work around the restrictions through relationships with local firms and the creation of India practice areas to manage inbound and outbound investments. While those practices have allowed firms such as Herbert Smith Freehills and Linklaters, whose India practices are based out of London and Hong Kong, to remain engaged with the Indian market, their roles still remain limited by current restrictions.

New rules have not been finalsed but a draft allows foreign law firms to form partnerships with local firms and to hire local lawyers. The timeline is elusive, though some say changes could come as early as this autumn. Liberalisation will almost certainly result in a flood of global law firms into the Indian legal market.

Latin America

Many firms report that expanding their role in Latin America is a top priority. Latin America's economies boast large commodities sectors, above-average GDP growth and strong economic ties to the US, Europe and China. And the region's legal markets look underpenetrated by global firms, creating the opportunity to grab market share.

A countervailing factor is the slowdown in the commodities market, which has hurt many local economies, and ongoing political turmoil in key countries. Overall, the region is seeing great growth in some areas and poor performance in others.

Brazil has been a disappointment for many global firms. There was hope that the country would become the region's financial capital, providing firms with a natural base to secure lucrative capital markets work and deal work throughout the region. But Brazil has been plagued by political and economic problems, slowing the development of corporate and finance practices. Yet trouble has buoyed demand for investigation work. Gibson Dunn & Crutcher, Paul Hastings and Cleary Gottlieb Steen & Hamilton have all secured leading roles on major investigations in Brazil in the past year.

Mexico has just one third the GDP of Brazil but it continues to be the largest market for Global 100 firms in Latin America. One reason is the country's deregulation of its energy markets. US firms have been particularly aggressive in this area, with Mayer Brown and Thompson & Knight opening energy-focused offices in Mexico City in the past year.

Other notable Latin American markets include Venezuela and Colombia. The collapse of the Venezuelan economy has created difficulties for many global firms and even caused some to rethink their presence. DLA Piper, for example, cut ties with its longstanding partner in Venezuela and decamped its Caracas partner to Miami. For firms that remain, the bulk of work is reportedly in debt restructuring, arbitration and employment.

The Colombian legal market, still largely dominated by local players, has much to offer global firms. The country has recently emerged from a longstanding civil war, has an investment-friendly government and boasts strong ties to the US economy. Those factors are creating a growing push in the country by global firms. Recent entrants include Dentons and Spanish-based Garrigues, which both announced mergers with local firms in the past year.

Africa

Global firms generally have focused on north Africa and South Africa. But they consistently report that they see significant potential in Africa's centre. That suggests that expansion is a matter of when, not if.

Firms' attraction to north Africa and South Africa is based largely on securing cross-border work. Natural resources work remains important in South Africa, though the country has developed into the sub-Saharan headquarters for international banks and development institutions, creating a steady stream of investment-related work.

Few firms have expanded elsewhere in Africa. An exception is Norton Rose Fulbright's entry into Tanzania in 2014. It is telling that the act was meant to be part of a broader push into central Africa, which never materialised. Baker & Mc­Kenzie also had plans to enter the region's markets but found difficulty in securing a local partner.

Firms' efforts to enter markets such as Kenya, Nigeria, Ghana and Mozambique have been stymied. Local firms report that they have been besieged with interest from global firms for partnerships and mergers. That has reportedly led many to hold out for sweeter deals. Also, the commodities slowdown has hurt many of the region's economies and weakened demand for legal services.

The future is clear, however. Sub-Saharan Africa is home to more than one billion people and key commodity-exporting countries. The region is also projected to be among the fastest growing. Satellite offices in north Africa and South Africa may work for the short term, but a more continent-wide strategy looks wiser in the long term.

• For more, see The Global 100: the world's top-ranked law firms by revenue, lawyers and partner profits