A FEW YEARS AGO, one of Charleston’s finest fishing boat captains approached chef Mike Lata with a problem: If business didn’t improve, he would have to hang it up. Federal quotas limited how much lucrative grouper and snapper he could catch, and while there were plenty of other fish for the taking, what he brought in barely sold for enough to cover gas. So, the chef made him a proposition:

“I told him on his next trip to bring us everything he caught, and we’d pay.” Mr. Lata and his cooks set to work on the catch—a grab bag of amberjack, banded rudderfish, mackerel, eel, lionfish and sea robin—and discovered that many of these fish were remarkably delicious. “This was great product, treated with care and attention, only the species names weren’t marketable. So, we decided to take care of the marketing side.”

Mr. Lata is one of a growing number of chefs making a case for eating abundant domestic species that have up until now been largely ignored. These are widely referred to as “trash fish,” a name originally bestowed by fisherman unable to sell them, now co-opted by some of their staunchest advocates.

The sea is home to thousands of fish species, but only a few of them regularly appear on American tables. Shrimp, tuna, salmon and tilapia together account for nearly 70% of seafood consumed in the U.S.; in the case of fine dining, cod, halibut and sea bass have also been in heavy rotation for the past 30 years. These once-plentiful species have retained pride of place on menus and behind fish counters long after it stopped making ecological sense, as chefs and seafood purveyors have catered to a dining public skeptical of trading salmon and swordfish for fish with names like “scup” and “smelt.”

Every fishery has a unique set of under-loved species. Waters in the Northeast are teeming with pollock, hake and dogfish, which match the flaky, mild profile of dwindling cod. Acadian redfish, once used for lobster bait off the coast of Maine, makes a superior alternative to tilapia, much of which is raised in antibiotic-spiked pools in China. The Chesapeake Bay is lousy with blue catfish, similar to the basa being imported by the ton from Vietnam. Firm, buttery and plentiful Pacific lingcod is a good understudy for pricey halibut. “There are incredibly delicious, vibrant, abundant fish out there and people don’t know about them,” said Michael Dimin, the co-founder of Sea to Table, a supplier to top seafood restaurants like New York’s Marea and RM Seafood in Las Vegas.