For some, the phrase “Dust Bowl” conjures a place: the Great Plains, but a Great Plains of abandoned homes, ruined lives, dead and dying crops and sand, sand, sand.

For others, the phrase denotes not a region but an era: the mid- to late-1930s in America, when countless farms were lost; dust storms raced across thousands of miles of once-fertile land, so huge and unremitting that they often blotted out the sun; and millions of American men, women and children took to the road, leaving behind everything they knew and everything they’d built, heading west, seeking work, food, shelter, new lives, new hope.

These families, immortalized in John Steinbeck’s The Grapes of Wrath and in the unflinching photographs of Dorothea Lange, Walker Evans and others, were almost universally known as “Okies,” whether or not they actually hailed from the devastated state of Oklahoma. The great, ragged migration away from half-buried farms and toward California and other vague “promised lands” is one of the defining catastrophes of the Great Depression. To this day, the very term Okie conjures images of gaunt men, grim women and doomed children dressed in tattered clothes, traveling by foot or jalopy across a landscape that seems perpetually dry, flat and ruined.

But just as entire families in Oklahoma, Texas, Colorado, Nebraska and other states abandoned their homes in search of a new start, countless other farmers held their own, suffering through the very worst of the Dust Bowl years, battling for every ear of corn, every grain of wheat, every leaf of lettuce on farms they had worked, in some cases, for generations.

Here, as massive, frightening droughts in California, Texas and elsewhere in the U.S. and abroad continue unabated, LIFE.com offers a series of revealing photos — most of which never ran in LIFE magazine — by the great Alfred Eisenstaedt. These pictures don’t follow “Okies” as they leave their world behind. Instead, Eisenstaedt’s photos chronicle the hardscrabble existence of Oklahoma farmers who stayed: families who fought to keep their livelihoods and their homesteads during those lean, unforgiving years after the Dust Bowl — according to the history books, at least — came to an end.

— Ben Cosgrove is the Editor of LIFE.com

Liz Ronk, who edited this gallery, is the Photo Editor for LIFE.com. Follow her on Twitter at @LizabethRonk.