Around 2.3 million Venezuelans -- 7.5 percent of the population -- live abroad, and 1.6 million of those have emigrated since the economic crisis worsened in 2015 -- the vast majority to other Latin American countries.
Here is a look at how Venezuela's hard-pressed neighbors have dealt with the issue so far, as ministers from a dozen Latin American states meet in Quito to try to forge a common response.
- No common policy -
In the absence of a coordinated policy, each country adopted its own measures to cope with what has bloomed into a major humanitarian crisis.
Venezuelans could previously move through nearby countries simply using their ID cards, but now, some countries have introduced visa or passport requirements to try to control the influx.
"It's a framework of restrictive measures that goes against human mobility, violates rights and increases the possibilities of insecurity via the threat of human trafficking," said Maria Amelia Viteri, migration researcher at Quito's San Francisco University.
- Open Borders? -
COLOMBIA: The migrants' main destination has taken in nearly a million Venezuelans so far, handing temporary residency status to 820,000. Venezuelans just need an ID card to enter.
ECUADOR: The country planned to introduce a passport requirement but was forced to suspend the move by a court order. It now requires an additional certificate issued by Venezuelan authorities -- or an international organization -- to authenticate the ID document.
Between January and August 2018, more than 641,000 Venezuelans entered Ecuador, with more than 524,000 moving on, according to the foreign ministry.
PERU: A booming economy makes it a magnet. Lima has tightened its border controls and imposed a passport requirement. In the last three years, 414,000 Venezuelans have entered.
CHILE: Chile introduced a visa requirement in April. It ensures residence for one year and access to employment contracts.
In the first six months of 2018, 124,450 Venezuelans entered Chile, compared to some 177,000 in all of 2017.
BRAZIL: Also lets Venezuelans enter the country with just an ID. Reports of growing xenophobia and violence against migrants in the border state of Roraima has prompted the government to deploy troops. Some 110,000 Venezuelans have arrived since last year, according to the most recent figures released in May.
BOLIVIA: Allows entry to Venezuelans with an ID card for a 90-day tourist visa. Since 2014, it has received some 25,600 Venezuelans. As everywhere else, the numbers are increasing here too.
URUGUAY: Allows in Venezuelans with an ID card, though those arriving by plane must carry a passport. In 2015, 1,100 Venezuelans applied for residence permits in Uruguay and the figure is increasing by 20 percent a year.
ARGENTINA: Home to 95,000 Venezuelans, including some 30,000 currently trying to regularize their stay.
CENTRAL AMERICA: With the exception of Costa Rica, all the Central American countries -- including the Maduro government's close ally Nicaragua -- demand a visa.
Last year, 27,000 Venezuelans asked for asylum in the United States -- almost twice as many as the year before and five times more than in 2016.
"Asylum claims have skyrocketed in recent years," Michael Bars, spokesman for the US Citizenship and Immigration Services (USCIS) told AFP.
"Our system is prone to legal loopholes, fraud and abuse, and this prevents legitimate asylum seekers from being prosecuted quickly," he said.
So far in 2018, nearly 16,000 Venezuelans have requested asylum.
Some 300,000 Venezuelans live in the United States, almost half in Florida.