The Mishna (Menachot 70a) lists the five species of grain. These species are of central importance in many halakhot. Only bread made from these species of grains is considered bread, and gets the brakha of hamotzi. Only matzah made from these grains is considered matzah, and can be used on the seder night. One only takes challah from bread made from these grains and no others. And it is only these grains which are forbidden prior to the bringing of the omer.
As the Gemara (70b) explains, the key principle here is fermentation. Only these grains ferment, and therefore only they can become chametz. Therefore, it is only dough from these grains which is forbidden, Biblically, on Pesach. The ability of the dough to become chametz, to leaven, is seen by the Rabbis as key to defining the product as bread, or even as bread's counterpart, matzah. Thus, in any halakha where the status of bread is significant, these grains will be the ones that matter.
Which grains, then, are we talking about? The Mishna lists five: wheat, barley, kusmin, shibolet shual, and shifon. These last three are generally translated as spelt, oats, and rye. However, for halakhic purposes, we need to be certain that these correct identifications. While the Gemara gives the Aramaic names for these three, these names are no more helpful than the Hebrew ones.
When it comes to shifon, Rashi translates this as sigala, which refers most likely to secale cereale, or rye. However, rye was unknown in the Land of Israel, and cannot be the right identification. Dr Yehudah Felix, author of "Flora and Fauna in the Talmud" (Hebrew), and many other scholarly works on ancient agriculture, concludes that shifon is Triticum spelta, or spelt, which is also the Arukh's definition. This is consistent with the fact that the braitta in the Gemara refers to shifon as a type of barley, and spelt has many characteristics which are similar to barley.
When it comes to kusmin, the Gemara translates this as gulba, which Rashi then translates as aspelta, which is spelt. However, given the above, this cannot be the right identification. Dr. Felix's conclusion is that kusmin is the same as kusemet, which is Triticum dicoccum, or emmer wheat (faro) which was in use in the land of Israel even before the First Temple period. This wheat was one of earliest cultivated forms of wheat, and this identification is consistent with the braitta which identifies kusmin as a form of wheat.
So we now have spelt and faro, but no rye. What about the third of these? Is shibolet shual truly oats, as is the common identification. Here the Gemara is not of any help, as the Gemara merely translates shibolet shual directly into Aramaic, as "fox stalk." Rashi, however, identifies it as avina, which is Avena sativa, or oats. This identification is problematic, however, because oats have no gluten. Remember that the Gemara stated that the key characteristic of these grains were their ability to become leaven. Rice and millet were excluded because they did not create leaven, and this is presumably because they have no gluten. Another reason to question this identification is that while some scholars do believe that oats grew in the Land of Israel in ancient times, almost all the evidence indicates that they did not.
What, then, is shibolet shual? Some scholars have suggested that it with sorghum. This is most likely incorrect, because it has no similarity to barley, the crop that it is considered by the braitta to be a sub-species of. Dr. Felix concludes that it is Hordeum distichum, a type of a two-row barley, as distinct from se'orim, which is a six-row barley.
So, where does all that leave us? According to this scholarship, the five species are: wheat, six-row barley, emmer wheat, two-row barley, and spelt.
Those interested in Dr. Felix's analysis of these grains, can see the selection from his commentary to Mishna Kilayim, from his book "Mixture of Seeds and Grafting" (Hebrew), on my Daf Yomi Blog under the Resources section.
Now, does this scholarship have any significance as far as halakha is concerned? This is not a trivial question since for people who have Celiac disease and are gluten-intolerant, the inclusion of oats as one of the five grains is of utmost importance. Since oats has no gluten - which was one reason to suspect their inclusion in the first place - their inclusion in the list allows gluten-intolerant people to have bread for hamotzi and to eat matzah on the seder night. Remember, that it was Rashi who identified shibolet shu'al as oats, and this identification was repeated by many Rishonim. We thus have a prime example of when science and halakha collide. Which do we follow? The traditional identification, or the one that scholars have concluded is the original and accurate identification?
A wonderful story illustrating this tension, exactly on our topic, is found on Hebrew Wikipedia under the topic chameshet minei dagan. Here is the story:
Professor Felix relates that on the basis of his identification, Rav Shlomo Zalman Aurbach, ztz"l, used to make the brakha of shehakol on his morning breakfast of oatmeal. He did this for two years until Rav Shalom Elyashiv yelled at him with the critique that one cannot change what has been the Jewish custom for hundreds of years, going back to the time of the Rishonim, just because of one scholar['s findings].
This conclusion actually reflects the basic way that halakha operates. While new information can be integrated and can lead to reassessment, nevertheless, there is a canonization process of certain works (e.g., the Babylonian Talmud) and certain interpretations (e.g., those of the Rishonim), which weigh the most heavily in halakha. In the end, the halakhic truth may diverge from the historical or scientific truth. Nevertheless, halakha is what books, authorities, and interpretations have been accepted as binding by the Jewish people committed to halakha. When conflicts between halakha and science or experience become blatant and incontrovertible, greater reassessment might take place. That is a discussion for another time.
In closing, it is interesting to compare the methodological issues raised here with those raised in our recent post on my daf blog on the prohibition of chadash. There, too, an objective analysis of the sources would lead to the conclusion that chadash is forbidden out of the Land of Israel and that we have to be scrupulous about it even today. Nevertheless, because it had been the practice for hundreds of years in Ashkenaz to not attend to the concerns of chadash, the poskim found various ways to justify the practice. There, as well as here, how halakha is lived, and the lived traditions around halakha, have ultimately more weight than the most technically accurate read of the sources.