Following a brief historical background, the concepts and the present state of sputter-depth profiling for thin-film analysis are outlined. There are two main branches: either the removed matter (as in mass- or optical-spectroscopy-based secondary-ion mass spectrometry or glow-discharge optical emission spectroscopy), or the remaining surface (as in Auger electron spectroscopy and X-ray photoelectron spectroscopy) is characterized. These complementary methods show the same result if there is no preferential sputtering of a component. The common root of both is the fundamental ion-solid interaction. Understanding of how the latter influences the depth resolution has led to important improvements in experimental profiling conditions such as sample rotation and the use of low-energy ions at glancing incidence. Modern surface-analysis instruments can provide high-resolution depth profiles on the nanometre scale. Mathematical models of different sophistication were developed to allow deconvolution of the measured profile or quantification by reconstruction of the in-depth distribution of composition. For the latter purpose, the usefulness of the so-called mixing-roughness-information (MRI) depth model is outlined on several thin-film structures (e.g. AlAs/GaAs and Si/Ge), including its extension to quantification of sputter-depth profiles in layer structures with preferential sputtering of one component (Ta/Si). Using the MRI model, diffusion coefficients at interfaces as low as 10(-22) m(2) s(-1) can be determined. Fundamental limitations of sputter-depth profiling are mainly traced back to the stochastic nature of primary-particle energy transfer to the sputtered particle, promoting atomic mixing and the development of surface roughness. Owing to more sophisticated experimental methods, such as low-energy cluster ion bombardment, glancing ion incidence or 'backside' sputtering, these ultimate limitations can be reduced to the atomic monolayer scale.