Illinois: 86 Ill. Adm. Code §§ 130.2080, 130 Illustration A, 480.101

86 Ill. Adm. Code 130.2080. Sales to Governmental Bodies, Foreign Diplomats and Consular Personnel.
a) Sales made to a governmental body (Federal, State, local or foreign) are exempt from the Retailers' Occupation Tax. Such sales are not exempt from the Retailers' Occupation Tax unless a governmental body has an active exemption identification number issued by the Department. However, retailers may accept U.S. Government Bank Cards in sales to the U.S. Government and its agencies without requiring an Illinois exemption number.
1) For the foregoing purposes, the date of sale is considered to be the date of delivery to the purchaser.
2) The purchase of meals, fuel and other tangible personal property by corporations in Illinois are taxable sales at retail, unless otherwise exempt, notwithstanding the fact that the stock of such corporations may be owned exclusively or in part by foreign governments.
b) When making a purchase, the holder of the card presents it to the retailer, who records the card number instead of collecting the tax.
c) The U.S. State Department, Office of Foreign Missions, issues tax exemption identification cards to accredited foreign diplomatic and consular officials. Under the authority of the Foreign Missions Act, various levels of exemption are authorized. Section 130.Illustration A depicts examples of the various cards currently being issued.

86 Ill. Adm. Code 130 Illustration A (Sales tax)
a) These are samples of the tax exemption cards issued by the U.S. Department of State to certain foreign government personnel and offices under the authority of the Foreign Missions Act (22 USC 4301 et seq.). The plastic cards, which are the size of credit cards and have a hologram, are valid nationwide. Cards are used at the point of sale for exemption from State and local sales taxes and similar taxes normally charged to customers. Some cards have restrictions on tax-free purchases. Tax exemption cards are not valid for exemption from taxes on telephones, other utilities, or gasoline purchases. Cards are not transferable. Only the person whose photograph appears on the front side of the card may use it. Vendors may ask for additional identification such as a driver's license.
c) Mission tax exemption cards are issued to embassies, consulates, and international organizations for official purchases only and for the sole benefit of the mission identified on the face of the card. All purchases must be made in the name of the mission and paid for by mission check or credit card (not cash or personal check). Personal purchases are prohibited when using a mission tax exemption card.

86 Ill. Adm. Code 480.101 (Hotel Operators’ Occupation Tax Act – Nature, Rate and Scope of the Tax)
b) Scope of the Tax – Examples of Taxability and Exemption
7) The Hotel Operators' Occupation Tax is not imposed upon gross rental receipts for which the hotel operator is prohibited from obtaining reimbursement for the tax from the customer by reason of a federal treaty (Section 3 of the Act). Under the Vienna Convention, some foreign diplomats are not required to pay reimbursement charges that are similar in nature to taxes. The exemption for rentals to certain diplomatic personnel applies only to diplomatic personnel possessing certain types of diplomatic tax exemption cards issued by the U.S. Department of State, Office of Foreign Missions. There are 2 types of diplomatic tax exemption cards: personal tax exemption cards and mission tax exemption cards. For each of these categories, 2 types of color-coded cards are issued: a blue-striped card that allows an individual or mission to make purchases exempt from all sales and use taxes and taxes on hotel rooms and a striped card of one of several other colors (yellow, green, red, or red-green) that allows an individual or mission to make tax-exempt purchases in all purchase categories except for the restricted purchase categories printed on the colored stripe. For examples, see 86 Ill. Adm. Code 130.Illustration A. In documenting this exemption, a hotel operator must obtain the mission's name, the card holder's name, the exemption number, the expiration date, and the color of the stripe on the card, or a photocopy of the diplomatic card.