To make it, fish is chopped up finely, mixed with a few other ingredients such as eggs to act as a binder, shaped into oblong patties (usually), then poached in a simmering liquid, then bottled.
“Gefillte” means filled. It used to be, the mixture was then stuffed back into the skin of a fish, which was then poached, and served in slices. This achieved two things: the fillers added to the chopped fish extended the amount of fish that could be served, making one fish go further, and, on Sabbaths, did away with the need for having to separate the fish meat from the bones, which some considered violating the Sabbath as it involved selection work. Putting the mixture back in the fish skin made it seem fancy, and that a whole fish was being served. Typically, it would be cooked in advance of Sabbath or other religious holidays, then served cold.
The fish used is usually a fresh-water fish, such as carp, pike, or other whitefish. Sometimes, mullet is used. To be kosher for Jewish dietary law, the fish used must have both scales and fins, and be inspected for fish worms (the fish is discarded if it is.) The eggs used as binder cannot have any blood spots in them.
There are many different recipes for gefilte fish.
Common to all is that the fish is skinned, cleaned and deboned first. The fish is then, traditionally at home, chopped and re-chopped, typically in a wooden bowl with a knife called a “Hockmesser”, adding a little cold water each time. Many people at home now of course just chuck it all into a food processor, but some say the texture comes out too smooth.
The chopped fish is then mixed, in some recipes, with eggs, and with matzo meal, to act as binders and bulkers, then seasoned. Seasoning typically includes minced onion. The mixture is then formed into patties, and cooked by simmering in a stock, either vegetable or fish (you can use the fish head, skin, bones, etc, for the fish stock.) There are often flavouring items such as carrot, celery, onion, etc, in the simmering water. After poaching, the fish balls are lifted out with a slotted spoon: the stock will set like a jelly when cool.
Gefilte fish is rarely made at home these days; most people buy it ready-made. The patties are sold in cans or bottles, packed in the jellied broth. You’ll find the bottles in the chiller sections at grocery stores. Many don’t like the jarred or canned versions; they consider them gloop.
You can also get it in frozen logs, wrapped in a waxed paper casing, or in vacuum packaging.
Commercial versions can be high in salt, though low-sodium versions are now available. There are also salmon and vegetarian versions now.
There is no set rule about how this commercially-prepared gefilte fish has to be served. Some serve it cold out of the fridge, almost always accompanied by a condiment called “chrain”, a vinegared horseradish mixture. In the UK, it is more common to drain the patties from the jelly and fry them to give the outside surfaces some crunch.
Sometimes sugar is added to the fish mixture, making it a bit sweet. Some people like this, some don’t. In fact, in the Jewish culinary map of Europe, there’s an imaginary boundary called “the Gefilte Fish Line.” Galitzianer Jews (historically from western Ukraine and the south-eastern corner of Poland ) added sugar; Litvak Jews (eastern Ukraine and Lithuania) preferred theirs more savoury, and so used no sugar.
Packaging forms in which gefilte fish may be served include: 
- Canned Gefilte Fish
- Bottled Gefilte Fish
- Jarred Gefilte Fish
- Gefilte Fish in Pouch
- Gefilte Fish in Tetra Pak
- Gefilte Fish in Dressing
- Marinated Gefilte Fish
- Gefilte Fish in Water
- Gefilte Fish in Oil
- Gefilte Fish in Brine
- Gefilte Fish in Sauce
- Gefilte Fish in Syrup
- Gefilte Fish in Spring Water
- Gefilte Fish in Vinegar
Gefilte Fish came out of the Ashkenazi Jewish tradition (Jews from Germany and Central Europe.)
Shortly before America joined World War Two, some food makers, particularly in New York, started selling prepared Gefilte Fish in cans, but the quality wasn’t judged highly.
Nathan Liebner, from southern Poland, started selling a higher quality canned version, in the sweet style. He called his canned products, “Mother’s Fish Products.” After the war, he switched to glass bottles instead, and others followed suit, notably the Manischewitz brand in 1954. 
One of the problems with the commercial versions, bottled or canned, was that the jelly tended to go liquid at room temperatures. A man named Monroe Nash got a US Patent (U.S. Patent #3,108,882) for his idea to add seaweed (carrageen) to the broth to make it more stable.
The broader American population first learned about Gefilte Fish through a Jewish sitcom called “The Goldbergs”, that ran on American TV from 1949 to 1956. It has never been broadly embraced, however, in the same way that smoked salmon or bagels have been.
Gefilte is a Yiddish word meaning “stuffed.” It comes from the German verb, “füllen”, meaning “to fill”, whose past tense is “gefüllt.”
 U.S. FDA FCE-SID Gefilte Fish Requirements. Accessed May 2016 at .http://www.registrarcorp.com/fda-fce-sample/Gefilte_Fish?lang=en
 Marks, Gil. Encyclopedia of Jewish Food. New Jersey: John Wiley & Sons. Page 222.
Dysch, Marcus. Glowing report for gefilte fish. The Jewish Chronicle Online. 24 September 2009.
Galst, Liz. Guilt-Free Gefilte Fish. OnEarth Magazine. 8 September 2010.
Gray, Marlene Sorosky. Gefilte fish made so easily, you’ll feel guilty. San Francisco Chronicle. 5 September 2010.
Kagan, Aaron. A Crispy Dish: Gefilte Fish, Fried to Perfection. The Jewish Daily Forward. 11 March 2009.
Nathan, Joan. Gefilte Fish: The Next Generation. New York Times. 12 April 2000.