Solutions to the EXAFS equation allow the determination of the structural parameters R, N and σ² from EXAFS data, provided that the scattering phase shifts, amplitudes and mean-free path terms are known. Even in the simplest form, the oscillatory nature of the EXAFS equation makes it intrinsically non­linear in the structural parameters, so that nonlinear least-squares methods are needed to find the most likely set of values for the structural parameters to best fit the EXAFS data. Such analysis methods have a substantial literature, are used in a broad range of scientific fields and have been demonstrated to lead to robust results for EXAFS analysis problems. In addition to finding the best-fit values, the methods generally give reliable estimates for the uncertainty in each of the variable parameters, taking into account the correlations between parameters. Still, the use of these methods requires some care, including legitimate concerns over uniqueness and the possibility of finding `false minima': solutions which match the data well but with parameter values that are not the correct solution. In this chapter, an overview of the practical application of these methods to EXAFS will be provided.