The commandment of tevila in the Torah was written regarding utensils made specifically of metal. The Torah writes that gold, silver, copper, iron, tin, and lead all require tevila.
Regarding other metals, such as aluminum or pewter, there are two opinions. The first opinion is that the Torah wrote about the common metals of the time, however, all metals are included in the commandment of tevilat keilim. The second opinion is that the Torah wrote these six metals to exclude all other metals. The other metals still require tevila with a bracha, however, it is only a rabbinic requirement.
Utensils made of stone, wood, pottery, and ivory do not require tevila, as the Torah specifies metal as the only material requiring tevilat keilim.
Glass, although not included in the biblical requirement for tevila, still requires tevila rabbinically. The Gemara explains that glass, like metal, is reusable when it breaks. Just like metal can be melted down and formed into a new vessel, so too glass. Therefore, our sages decreed that glass is included in the commandment of tevilat keilim.
Plastic is a subject of debate among the later poskim. Some rule that since our sages decreed that glass be included in tevilat keilim rabbinically because it can be melted down and reused, so too plastic which can be melted down and reused would be included in tevilat keilim rabbinically. However, the vast majority of Poskim rule that plastic does not require tevila. Even though our sages ruled that glass requires tevila, we cannot add new components to such rabbinic edicts.
China, porcelain, and ceramic do not require tevila, since they are the same category as pottery. However, if they are coated in glass, they do require tevila to kosher the glass coating. One should check carefully when buying dishes as it is very common for there to be a coating, either for durability or to prevent staining of the dishes.
 ערה”ש יו”ד סי’ קכ סעי’ כג
 אג”מ יו”ד ח”ג סי’ כב
 רמב”ם מאכ”א פי”ז הל’ ו
 שו”ע יו”ד סי’ קכ סעי’ א, ועי’ ערה”ש שם סעי’ כד, ומשנ”ב סי’ תקט ס”ק ל
 עבודה זרה עה:
 מנחת יצחק ח”ג סי’ עו-עח, חיי הלוי ח”ד סי’ נו אות ג
 חזו”א ארחות רבינו ח”ג עמ’ עה, באר משה ח”ב סי’ נג, חוט שני טבילת כלים עמ’ כו-כז
 עי’ פת”ת יו”ד סי’ קכ ס”ק ב, ערה”ש שם סעי’ כט