This paper reviews the current status of free-air ionization chamber standards for the determination of air kerma in low- and medium-energy x-rays. It describes the underlying definitions and concepts that permit the air kerma to be determined from a measurement of the charge produced in a free-air chamber. The most commonly used design, the parallel-plate free-air chamber, is discussed in detail, in particular with a view to optimization of the design parameters to minimize the overall uncertainty of the air-kerma determination. Various correction factors and their uncertainties are discussed, with an emphasis on the use of the Monte Carlo technique in the evaluation and optimization of certain corrections. Alternative free-air chamber designs are outlined. The results of international comparisons of free-air chamber standards are presented.