The design and operation of the vapor-absorption refrigerator (VAR) are described using the principles and tools typically covered in upper-division undergraduate physical chemistry courses. The objective is to enable students to understand in detail how this device works and how it compares with more typical vapor-compression refrigerators. Calculations of the thermodynamics and heat flow relating to the refrigeration cycles are presented, leading to the calculation of the coefficient of performance. Two types of VARs are examined, one using LiBr/water solution as the absorbing medium and water as the refrigerant, which relies on the hygroscopic nature of aqueous solutions of LiBr. The second uses water as the absorber and ammonia as the refrigerant. The device described, the Crosley IcyBall, was a popular and inexpensive home refrigerator requiring no electricity. It is an example of a VAR operating in a single-cycle mode.