They have risked drowning, shooting, and the brutal attack of pirates. They have traded persecution or poverty for a dream of prosperity and the reality of an uncertain future.
In the last few years hundreds of thousands of these Indochina refugees have swum, trekked, or sailed their way on the long voyage to eventual resettlement in Australia, the United States, and Europe.
Now there are some signs that the door of history may soon close on the third great outpouring of Indochinese refugees since World War II.
The reasons involve a reduction of both the ''push factors'' forcing people to leave and the ''pull factors'' such as preferential quotas that lure many to think they will be accepted in prosperous countries like the United States:
* Countries of ''first arrival'' such as Thailand and Malaysia are clamping down on the entry of refugees, who are more and more often being turned away on grounds they are ''economic migrants.''
It is too soon to know the full impact. But some refugee officials predict that as word of the clampdown gets back to Vietnam, fewer ''boat people'' will depart. Already the flow of Lao refugees has slowed to a trickle.
* The lure of resettlement in prosperous countries has dimmed somewhat, as countries like the US debate whether quotas should be lowered to screen out ''economic migrants.'' Arguing that decreasing refugee outflow means lower quotas are in order, the US has already slashed its Indochina resettlement quota from a maximum of 168,000 last year to a maximum of 100,000 for the coming year.
* Vietnam has stiffened prison sentences for those caught planning to leave. This, plus signs that Hanoi is proving more cooperative on the ''orderly departure'' program to allow legal emigration of some citizens, has reinforced the conclusions of US State Department refugee officials who predict a gradual decline in Vietnamese refugee flow.
* Food conditions in Cambodia have vastly improved, compared to 1979 and 1980 - when famine sent hundreds of thousands of refugees fleeing by foot and oxcart to relief centers on the Thai border. Many of the 500,000 Cambodian refugees ''floating'' on the border in early 1980 have dispersed back into Cambodia. With about 220,000 ''floaters'' (Cambodian refugees not in resettlement camps) today, a US State Department spokesman terms the problem still ''substantial'' but not at ''crisis level.''
Better food conditions in Cambodia and Thai reluctance to accept new arrivals as ''refugees'' have slowed the flow.
These conclusions must be treated with caution. New political and economic upheavals could reopen the tap. The number of Cambodian ''floaters'' on the Thai border is up 50,000 over four months ago, as a result of water and crop shortages, as well as fighting in some parts of Cambodia.
Some refugee declines may reflect seasonal influences such as changing winds which hamper boat departures from Vietnam or changing water levels which make it harder for Lao refugees to cross the Mekong River into Thailand.
Ups and downs sometimes seem to defy trends. Only 81,000 Vietnamese boat people reached Southeast Asian camps in 1981, compared with 245,000 in 1979. Still, that is a slight increase over some 64,000 in 1980. On balance, however, the US State Department predicts an overall decline in boat people leaving Vietnam in 1982.
Even if refugee flows continue to slow, the task of resettling, training, and finding jobs for those already in Southeast Asian camps is formidable.
As of September 1981 there were some 271,000 Indochina refugees in these camps, according to US State Department figures.
This is still encouraging compared to some 356,000 in Southeast Asian camps in September 1980.
The first great flow of Indochina refugees followed the 1954 French defeat by of Vietnam's communists. Thousands of anticommunists fled from communist North Vietnam to noncommunist South Vietnam - or emigrated to countries like France and the US.
The second great flow followed the 1975 communist victories in Cambodia, Laos , and South Vietnam, when anticommunists in all three countries fled to the US and France.
The third great upsurge, between 1978 and 1980, reflected poverty and dislocation caused by the the socialization of southern Vietnam's economy. Some 80 percent of the boat people leaving Vietnam were ethnic Chinese facing persecution as growing hostility led to brief war between China and Vietnam in early 1979. In the same upsurge Cambodian refugees fled the political chaos and famine that followed Vietnam's early 1979 invasion of Cambodia.
In Laos, declining living standards caused a continuing wholesale exodus of the middle class, lured as they were by the ease of crossing the Mekong River into less austere Thailand. Also in Laos, Vietnamese-backed military campaigns to subjugate the formerly American-supported Hmong hill tribes led many of these people to retreat across the Mekong into Thailand.
Now that much of this is in the past, some of the ''push factor'' behind the exodus is gone. Most of the ethnic Chinese willing and able to leave Vietnam have left. Most of the Hmong tribesmen able and eager to leave Laos have crossed the Mekong. Cambodia's famine is no longer nationwide.
Vietnam appears increasingly cooperative in efforts to allow the legal emigration of Vietnamese citizens to countries which accept them under ''orderly departure,'' according to both US and Australian officials.
''We think it is realistic to hope for upwards of 1,000 a month to the US alone,'' a State Department official comments.
After prolonged wrangling over the kind of people who should come, the first successful mutually agreed upon ''orderly departure'' exodus from Vietnam to the US took place from November 1980 to February 1981. Some 1,300 left for the US, until Vietnam shut off the flow and began to reevaluate the program. Other involved countries also encountered similar difficulties. Then, in early October , Vietnamese refugee officials met in Geneva with representatives of the US and other countries involved in the program. The outcome, according to participants, was positive.
At about the same time the flow to the US has begun again, including more than 100 in the last month. Altogether some 7,500 Vietnamese have left under the program, headed for some 15 countries.
There is also a prospect that a large number of Cambodian refugees can be returned voluntarily to their homeland. About one-third of some 100,000 Cambodians in Thai refugee camps (as opposed to the 220,000 ''floaters'') would be willing to return, according to a US State Department spokesman.
Cambodian government representatives meeting in Bangkok with officials of the United Nations office of High Commissioner for Refugees have expressed willingness to welcome back the refugees. Many of these are are not political opponents but farmers who fled famine to find food. Some experts say their skills are now needed to help rebuild Cambodia's economy.
Laos has actively sought to encourage the return of refugees whose skills are desperately needed. Although several hundred have returned, many more have refused out of doubts they will be trusted, or rewarded in an austere backward economy dominated by a Vietnam-aligned Communist Party.
Vietnam has shown no interest in repatriation of refugees. It appears convinced that most of those who leave are a political and economic burden. Its response is an apparent sigh of ''good riddance.''
Hanging over all this is the increasingly ''closed door'' attitude toward more refugees shown by Indochina's neighbors.
In spring 1981 Thailand closed the relatively comfortable Nongkhai resettlement camp for Lao refugees and opened a more austere center in Napha. This has sharply reduced the flow of Lao refugees.
In August a high-ranking Thai official described most arriving Vietnamese refugees as ''economic adventurers'' out to get a higher standard of living. At the same time Thailand announced that thereafter boat people landing in Thailand will not be eligible for resettlement to third countries such as the US. Thailand also closed off to Vietnamese boat people a major landing point and port of refuge, the southern city of Songkhla.
Refugee officials say it is too early judge whether these measures, aimed at decreasing the ''pull factor,'' will work. One possible result is that would-be refugees, knowing they are unwelcome in Thailand, will navigate their boats either north to Hong Kong or south toward Malaysia and Indonesia.
If so, there will be a spillover effect and other countries will be under increased pressure to make their regulations even stricter.
Malaysia has already taken the point. After 40 Vietnamese refugees recently landed on Malaysia's east coast from the South China Sea, Kuala Lumpur was reported to have stepped up naval patrols to head off any possible new refugee influx.