The shop was founded by Murray Bernstein in 1945.[2] A few years later, his brother, Sam, became a co-owner.[2] The Bernsteins were born in Poland and immigrated to New York in the 1930s to escape anti-semitism.[2]
The store specializes in smoked fish, especially sturgeon, and caviar.[2][3] In 1964, The New York Times described it as "one of the busiest places on Broadway" and praised its products as "first quality".[3] The store ships their fish all over the world, and in 1980 Murray's appetizers were being sold at the Neiman Marcus Epicure Shop in White Plains, New York.[4]
In 1974, the shop was sold to restaurateur Artie Cutler. Artie took in a partner, Harold "Heshy" Berliner, in 1979. They sold the business to Ira Goller in 1990.[6]
Sam Bernstein died in 1977 and Murray Bernstein died in 2000.[2][5]