Gemara

(Rav Nachman): Bone Kelim are like metal Kelim.

Question: This implies that bone Kelim can become Tamei. What is the source for this?

Answer (Beraisa - R. Yishmael, son of R. Yochanan ben Brokah): "You will sprinkle (water with ashes of the Parah Adumah) everything made from sheep" includes things made from the horns and hooves.

98a (R. Chiya bar Aba, citing Bar Kapara): Any Isur in the Torah is Batel among 60 parts of Heter.

(R. Shmuel bar Rav Yitzchak): Rav Asi cited Bar Kapara to say that it is Batel among 100 parts of Heter.

Both learn from (Bitul of) the foreleg of Eil Nazir. It is forbidden to a Zar (non-Kohen), and (at least according to R. Shimon) it is cooked with the ram. (Zarim may eat the ram).

The first opinion holds that the taste of the meat and bones of the foreleg are Batel amidst the meat and bones of the ram (which are 60 times as much);

The latter opinion learns from Bitul of the meat of the foreleg among the meat of the ram (which is 100 times as much).

Pesachim 30b: The Halachah is, to Kasher a knife, it suffices for the blade and handle to be in boiling water in a Kli Rishon.

(Rav Huna brei d'Rav Yehoshua): A wooden mixing spoon may be Kashered in boiling water in a Kli Rishon.

83a (Gemara - Rav Mari bar Avuha): Bones of Kodshim that once held Nosar (marrow) are Metamei hands, because they once held something forbidden.

(Mishnah): Bones, sinews and Nosar of Pesach are burned on the 16th.

Question: If the bones do not have marrow, why must they be burned? One may discard them!

Answer: Rather, they have marrow. They must be burned because holding Nosar is significant.

Shabbos 16b: Tum'ah of metal vessels is mid'Oraisa - "Ach Es ha Zahav v'Es ha'Kesef..."

Avodah Zarah 74b (Mishnah): If a Nochri applied pitch to a stone winepress, it suffices to (rinse and) dry it.

Rebbi says, if it is made of wood, it suffices to dry it;

Chachamim say, he must peel off the pitch.

If it is made of Cheres (earthenware), even if he peels off the pitch it is forbidden.

75a (Beraisa): To be Metaher a winepress or olivepress (used with Tamei wine or oil), one must rinse the boards, brooms and tub.

The same way we are Metaher, we Kasher from Yayin Nesech.

75b (Beraisa): If one buys from a Nochri a Kli used for food, it must be immersed in a Mikveh of 40 Sa'im.

(Rava): We learn from "Kol Davar Asher Yavo ba'Esh Ta'aviru ba'Esh v'Taher" - the Torah requires an additional Taharah after Kashering.

(Bar Kapara - Beraisa) Suggestion: Perhaps "b'Mei Nidah Yischata" teaches that one must sprinkle on it on the third and seventh day!

Rejection: "Ach" excludes this.

"B'Mei Nidah" teaches that he must immerse it in water that a Nidah could immerse in, i.e. a Mikveh of 40 Sa'im.

Rishonim

The Rif and Rosh (Pesachim 8b and 2:7) bring the Gemara in Pesachim.

Rambam (Hilchos Chametz 5:23): Kelim of metal or stone that were used for hot Chametz in a Kli Rishon, e.g. pots and pans, one puts them in a big Kli and fills it with water and boils the water inside it.

Rambam (24): Kelim of metal or stone or wood that were used for Chametz in a Kli Sheni, e.g. bowls and cups, one puts them in a big Kli and pours boiling water on them.

Rashi (98b DH u'Man): The latter opinion omits the bones from the calculation, for they do not emit taste.

Mordechai (Pesachim 582): Or Zaru'a says that bone Kelim do not require Hag'alah, for they do not absorb. If one inserted a dairy bone spoon into a pot of meat, even if the spoon was Ben Yomo (used for hot milk in the previous 24 hours), even if there was not 60 times the volume of the spoon in the pot, it does not forbid. It never absorbed milk, so it does not emit. Also R. Yechi'el of Paris says that we do not find absorptions and Isur regarding bone Kelim. I act in practice like I wrote.

Hagahos Rema (perhaps this is from his Talmid, the Levush) :Also Rashi connotes like this. Another proof is from Pesachim 83a. We obligated burning bones only because they were a basis for Isur, but not because they themselves absorbed taste. This shows that they do not absorb.

Mordechai: However, I am hesitant. In Parshas Midyan, it says "and everything made from sheep", and Rashi (Bamidbar 31:20) says that this includes the horns, hooves and bones. All the more so we include Kelim of bones or horns of a big ox. This shows that bone Kelim absorb, since the Torah says Tischata'u! Also Chulin 25a says so.

Chachmas Shlomo (OC 451:8): What is the proof from Klei Midyan? The verse discusses immersing the Kelim! The verses after this discuss Kashering (and they mention only metal Kelim)! To resolve this, I say that Kelim that do not absorb do not receive Tum'ah mid'Oraisa, rather, only mid'Rabanan (Shabbos 15a).

Note: Shabbos 15a merely says that Chachamim decreed Tum'ah on glass Kelim. It does not mention absorption.

Chachmas Shlomo: Shabbos 16b learns Tum'ah of metal Kelim from "Ach Es ha Zahav v'Es ha'Kesef..." The verse discusses Kashering! Even though it says "Ta'aviru ba'Mayim", that refers to immersing (even) new Nochri Kelim used for food, but not immersing due to Tum'ah (Avodah Zarah 75b). How is this a source for Tum'ah? Rather, we must say that since (it must be Kashered, this shows that) it absorbs, this shows that it is Mekabel Tum'ah. Conversely, anything that is Mekabel Tum'ah (mid'Oraisa) absorbs.

Note: Rashi (Bamidbar 31:23) says that the simple reading of "b'Mei Nidah Yischata" obligates Taharah from Tum'ah; Chachamim expounded it to teach about immersing even new Kelim. If the simple meaning is also true (it seems to me that Rashi holds like this), Chachmas Shlomo's proof is invalid.

Chachmas Shlomo: The Mordechai did not bring a proof from the Mishnah (Kelim 2:1) that says that bone Kelim are Mekabel Tum'ah. This is because one could say that this is only mid'Rabanan, like Tosfos (Chulin 25b DH Michlal) says.

Mordechai (585): A Tosefta in Zevachim (10:6) says that stone Kelim do not need Merikah and Shetifah (rinsing and scouring); it suffices to rinse. 'Rinse' means Hag'alah. Sefer ha'Mitzvos says so.

Tur (OC 451): Kelim of wood, stone or metal are the same. They are Kashered through Hag'alah. R. Yitzchak says that Shetifah (rinsing) suffices to stone Kelim. Rav Hai Gaon says that if they are used with boiling water, Hag'alah does not suffice. One must heat them in an oven until they are glowing hot. The Rif equates all of these.

Ra'avan (Teshuvah 8): We learn Isur from Tum'ah. In Avodah Zarah we say that the same way we are Metaher, we Kasher from Yayin Nesech.

Poskim

Shulchan Aruch (OC 451:8): Kelim of wood, stone or metal are Kashered through Hag'alah.

Beis Yosef (DH Ein): The Rif, Rambam and Rosh do not distinguish Kelim of wood, stone or metal. This is the custom.

Gra (DH Echad): The Torah explicitly says that metal Kelim must be Kashered. Wood and stone Kelim are like metal Kelim. This is unlike Rav Hai Gaon, who says that they are like Kli Cheres (earthenware), and they must be fired in an oven. A proof (for the Mechaber) is that in Avodah Zarah (74a), the Mishnah teaches how to Kasher stone and wood, and says that Cheres is different. A Mishnah (Kelim 5:11) says that an oven of stone or metal is not Tamei like an (earthenware) oven (i.e. through its airspace), but it is Tamei like a metal Kli. Ra'avan says that we learn Isur from Tum'ah, like it says at the end of Avodah Zarah. However, a Tosefta (Zevachim 10:6) says that stone Kelim do not need Merikah and Shetifah (rinsing and scouring); it suffices to rinse. The Mordechai (Pesachim 585) said that 'rinse' means Hag'alah. This is difficult. Further, the opinion (Zevachim 96b) that Merikah is in hot water says so because it is Hag'alah!

Dameshek Eliezer (33): Perhaps we can explain the Tosefta to means that stone Kelim do not need Merikah in water. One may use wine or mixed wine. Alternatively, they do not require Hag'alah unless they were used for cooking.

Mishnah Berurah (56): A wooden Kli can be Kashered only if it is smooth without any crack or cavity.

Kaf ha'Chayim (124): The Taz (24) says so.

Rema: Also Kelim of bone require Hag'alah.

Bach (9 DH Kasav): The Tur brings that Sefer ha'Manhig says that one cannot Kasher horn (ivory) spoons. If so, one cannot Kasher knives with an ivory handle through Hag'alah. The Maharil (Hilchos Hag'alah 23:14) says so. Mahariyo (193) says 'one opinion holds that one cannot Kasher bone Kelim, for he is concerned for them (lest they get ruined), and he will not Kasher them properly. I hold that the same applies to knives with bone handles, or even of wood. Since the handle is glued on, he is concerned.' Perhaps he does not rule like this; he just says that the one who forbids to Kasher bone Kelim, should also be stringent about knives with bone handles. One who is stringent for himself will be blessed. Letter of the law, Hag'alah suffices for bone Kelim, like most of our Rebbeyim say.

Bach (9 DH u'Mah): The Tur said 'the Rif equates all of these', i.e. Kelim of wood, stone and metal, which the Tur initially discussed. The Rif does not discuss ivory Kelim in the entire Perek. We do not find anyone who disagrees with ha'Manhig. The Kolbo (48:9:4) says that Rashi says that k'Bol'o Kach Polto (just like it absorbs, it emits), and just like the entire year one is concerned for it and does not put it in a boiling pot lest it get ruined (so one need not Kasher it). This is a great leniency. Perhaps while using it during the year, he unknowingly used it also with truly boiling water. While Kashering, he is concerned for it and does not put it in truly boiling water. The Manhig's opinion is primary. This is the custom.

Gra (DH v'Chen): This is like we say in Chulin, that bone Kelim are like metal Kelim.

Mishnah Berurah (57): An ivory Kli is excluded. Since it is soft and he is concerned lest it get ruined, Hag'alah does not help for it.

Kaf ha'Chayim (126): Similarly, Hag'alah helps for leather Kelim, and everything except for Cheres. Kelim of paper and cloths are permitted only through laundering in hot water with ashes (soap) and banging. Hag'alah does not help for what is intact and absorbed in the holes in the weaving.