In order to perform a structural analysis of extended X-ray absorption fine-structure (EXAFS) data, the fine structure must be extracted from the measured absorption coefficient μ(E). The EXAFS or differential absorption χ(E) is commonly defined as [μ(E) − μ₀(E)]/μ₀(E), where μ₀(E) is a smooth function of energy E representing the absorption from the idealized isolated absorbing atom. Unfortunately, it is not always easy to distinguish which parts of μ(E) are due to structurally derived EXAFS and which parts are due to the atomic or electronic excitations that comprise μ₀(E). If not performed carefully, the removal of the `background' μ₀(E) can significantly impact the EXAFS oscillations in χ(E) and the results of the structural analysis. The details of mathematical determination of the EXAFS background μ₀(E) are discussed and examples are given to illustrate the common strategies for background removal of EXAFS data.