Cheesecake is a dessert made with a soft fresh cheese (typically cottage cheese, cream cheese, quark or ricotta), eggs, and sugar. It may have a crust or base made from crushed cookies (or digestive biscuits), graham crackers, pastry, or sometimes sponge cake. Cheesecake may be baked or unbaked, and is usually refrigerated.
 Vanilla, spices, lemon, chocolate, pumpkin, or other flavors may be added to the main cheese layer.  Additional flavors and visual appeal may be added by topping the finished dessert with fruit, whipped cream, nuts, cookies, fruit sauce, chocolate syrup, or other ingredients.
 Modern cheesecake is not usually classified as an actual "cake", despite the name (compare with Boston cream "pie"). Some people classify it as a torte due to the usage of many eggs, which are the sole source of leavening, as a key factor. Others find compelling evidence that it is a custard pie, based on the overall structure, with the separate crust, the soft filling, and the absence of flour.[failed verification]  Other sources identify it as a flan, or tart.
 Smoked salmon cheesecake is a savoury form, containing smoked salmon.  It is most frequently served as an appetizer or a buffet item. A smoked salmon cheesecake was a prize-winning recipe in 1996 in Better Homes and Gardens' Prize Tested Recipe Contest.  The recipe called for the use of Swiss cheese along with the more usual (for cheesecakes) ricotta.
 An ancient form of cheesecake may have been a popular dish in ancient Greece even prior to Romans' adoption of it with the conquest of Greece. The earliest attested mention of a cheesecake is by the Greek physician Aegimus (5th century BCE), who wrote a book on the art of making cheesecakes (πλακουντοποιικόν σύγγραμμα—plakountopoiikon sungramma). The earliest extant cheesecake recipes are found in Cato the Elder's De Agri Cultura, which includes recipes for three cakes for religious uses: libum, savillum and placenta. Of the three, placenta cake is the most like modern cheesecakes: having a crust that is separately prepared and baked.
 A more modern version called a sambocade, made with elderflower and rose water, is found in Forme of Cury, an English cookbook from 1390. On this basis, the English chef Heston Blumenthal argues that cheesecake is an English invention.
 The English name cheesecake has been used only since the 15th century, and the cheesecake did not evolve into its modern form until somewhere around the 18th century. Europeans began removing yeast and adding beaten eggs to the cheesecake instead. With the overpowering yeast flavor gone, the result tasted more like a dessert treat. The early 19th-century cheesecake recipes in A New System of Domestic Cookery by Maria Rundell are made with cheese curd and fresh butter. One version is thickened with blanched almonds, eggs and cream, and the cakes may have included currants, brandy, raisin wine, nutmeg and orange flower water.
 Modern commercial American cream cheese was developed in 1872, when William Lawrence, from Chester, New York, was searching for a way to recreate the soft, French cheese Neufchâtel. He discovered up with a way of making an "unripened cheese" that is heavier and creamier; other dairymen came up with similar creations independently.
 Modern cheesecake comes in two different types. Along with the baked cheesecake, some cheesecakes are made with uncooked cream cheese on a crumbled-cookie or graham cracker base. This type of cheesecake was invented in the United States.
 Cheesecakes can be broadly categorized into two basic types: baked and unbaked. Some do not have a crust or base. Cheesecake comes in a variety of styles based on region:
 One popular variant of cheesecake in South Africa is made with whipped cream, cream cheese, gelatin for the filling, and a buttered digestive biscuit crust. It is not baked, and is sometimes made with Amarula liqueur. This variant is very similar to British cheesecake. This cheesecake is more common in British South African communities.
 Japanese cheesecake, or soufflé-style or cotton cheesecake, is made with cream cheese, butter, sugar, and eggs, and has a characteristically wobbly, airy texture, similar to chiffon cake. No-bake cheesecakes are known as rare cheesecake (Japanese: レアチーズケーキ).
 The most prominent version of cheesecake in the Philippines is ube cheesecake. It is made with a base of crushed graham crackers and an upper layer of cream cheese and ube halaya (mashed purple yam with milk, sugar, and butter). It can be prepared baked or simply refrigerated. Like other ube desserts in the Philippines, it is characteristically purple in color.
 Crostata di ricotta is a traditional Italian baked cheesecake, made with ricotta cheese, chocolate chips and eggs. Also many cakes and desserts are filled with ricotta, like cassata Siciliana and pastiera Napoletana.
 Basque cheesecake was created in 1990 by Santiago Rivera of the La Viña restaurant in the Basque Country, Spain. It is composed of burnt custard and no crust. It achieved popularity online in the 2010s, helped by a recipe published by the British food writer Nigella Lawson. The Spanish chef Nieves Barragán Mohacho serves hers with a liquorice sauce, which Lawson included in her recipe. 
 In 2021, Basque cheesecake was widely shared on Instagram and became "ubiquitous" in the UK. In 2023, the British restaurant critic Jay Rayner complained that Basque cheesecake had become overabundant in London.
 Swiss Chäschüechli (ramequin in French-speaking parts of the country) are small cheesecake tartlets, savory rather than sweet.
 The United States has several different recipes for cheesecake and this usually depends on the region in which the cake is baked, as well as the cultural background of the person baking it.
 Chicago-style cheesecake is a baked cream cheese version that is firm on the outside with a soft and creamy texture on the inside. These cheesecakes are often made in a greased cake pan and are relatively fluffy in texture. The crust used with this style of cheesecake is most commonly made from shortbread that is crushed and mixed with sugar and butter. Some frozen cheesecakes are Chicago-style.
 New York–style cheesecake uses a cream cheese base, also incorporating heavy cream or sour cream. The typical New York cheesecake is rich and has a dense, smooth, and creamy consistency.[better source needed]
 Sopa paraguaya is a salty cheese cake or bread that is the national dish of Paraguay; it is made with Paraguayan cheese and maize.[citation needed]