Etrog
Etrog, ethrog or esrog are all different pronounciations of the word , which is the most common Hebrew name for the citron or Citrus Medica.
It is one of the four species used in a waving ritual during the Jewish holiday of Sukkot. The other species are the lulav (date palm frond), hadass (myrtle bough), and aravah (willow branch).
Leviticus 23:40 refers to the etrog as pri eitz hadar (  ), which literally means, "a fruit of the beautiful tree." Modern Hebrew translates hadar as "citrus" in connection with the rabbinical definition of the etrog as the fruit referred to by the Torah. However, the commentary of Nahmanides states that the word "Hadar" was the original Hebrew word for the citron solely. The name was later replaced by the word Etrog meaning love and attraction in Talmudical Aramaic, which was initially adapted in Babylonia after destruction of the First Temple. The Arabic name for the fruit itranj  is also cognate with the Hebrew; the itranj is mentioned favorably in the Hadith. Similar names like "turunj" etc. are found in different languages.
The etrog is typically grown from cuttings that are two to four years old; the tree begins to bear fruit when it is around three years old. If the tree germinates from seeds, it will not fruit until about seven years. Besides, there might be some genetic changes to the tree and its fruits, whenever seed propagation is used.
The fruit is ready to harvest when it reaches six inches in length, for the best marketing, and is typically picked off the tree while it is still green.  Its inner rind is much wider than the pulp. The outer surface is somewhat hard and fragrant; the pulp should be dry, and may vary from sweet to strongly acidic, depending on the variety.
According to Halakha, the etrog used in the mitzvah of the four species must be largely unblemished and of a nice form and shape. Extra special care is needed to cut around the leaves and thorns which may scratch the fruit. Also, the bearing branch should be curved in order to get the fruit growing in a straight downward position. Otherwise, the fruit will be forced to make the curve on its own body when turned downwards because of its increasing weight.
An etrog that still has a pitom at its tip (a pitom is composed of a style called in Hebrew "dad", and the stigma which is called shoshanta, and it usually falls off during the growing process) is considered especially valuable. However, those varieties that shed their pitom during growth, just like other citrus species, are also kosher. Even when the stigma break off post harvest, it could still be considered kosher as long as part of the style is remained attached.
There is a custom amongst some Hasidim to take an etrog with a gartel (an hourglass-like waist running around the middle). Talmudic sources do not comment on this.
The marketability of the etrog depends on its form, cleanliness, and the condition of the apex of the fruit. According to some opinions, it shouldnt be taken even from the cuttings of a grafted tree.
The primary mitzvah of using the etrog is to take it along with the rest of the four species before and during the Hallel prayer. After the holiday, some people boil the peel of the etrog to make jam, fruit cake, and candied fruit. Some people also slice the etrog thinly and add it to a bottle of vodka in order to make an interesting libation. There is an Ashkenazic tradition to eat the etrog in the sacred day Tu B'Shevat, in order to maximize the variety of fruits eaten on that holiday to praise the Creator of the trees, and to establish a prayer to God to provide a nice clean non-grafted nor hybridized etrog for the next Sukkot.

# Confusion
There is some confusion in the secular world, because the specific variety originating from the Corfu Island, and nowadays the leading cultivar in Israel, is the only one to be called etrog in order to be used for the Jewish ritual. This was generally influenced by the botanical name of the variety, which is called variety etrog.
In fact, the use of the Corfu variety was disputed during centuries and so were their descendants in Israel. In any case, many varieties were traditionally used for the Feast of Tabernacles, and may even be rather recommended.

# DNA studies
A general DNA study was arranged by the world known researcher of the etrog, Pro. E.E. Goldschmidt & colleagues, who positively testified 12 known accessions of citron for purity and being genetically related. This is all about genotypeic classification which could be changed by breeding for e.g. out cross pollination etc., not about grafting which is not suspected to change any genes. (The above Greek citron was not included in that study).
A brief documentation of this study could be found at the Global Citrus Germplasm Network.

# The etrog in popular culture
The purchase of a beautiful (and expensive) etrog forms an important plot point in the film Ushpizin.