The analysis of thin films is of central importance for functional materials, including the very large and active field of nanomaterials. Quantitative elemental depth profiling is basic to analysis, and many techniques exist, but all have limitations and quantitation is always an issue. We here review recent significant advances in ion beam analysis (IBA) which now merit it a standard place in the analyst's toolbox. Rutherford backscattering spectrometry (RBS) has been in use for half a century to obtain elemental depth profiles non-destructively from the first fraction of a micron from the surface of materials: more generally, "IBA" refers to the cluster of methods including elastic scattering (RBS; elastic recoil detection, ERD; and non-Rutherford elastic backscattering, EBS), nuclear reaction analysis (NRA: including particle-induced gamma-ray emission, PIGE), and also particle-induced X-ray emission (PIXE). We have at last demonstrated what was long promised, that RBS can be used as a primary reference technique for the best traceable accuracy available for non-destructive model-free methods in thin films. Also, it has become clear over the last decade that we can effectively combine synergistically the quite different information available from the atomic (PIXE) and nuclear (RBS, EBS, ERD, NRA) methods. Although it is well known that RBS has severe limitations that curtail its usefulness for elemental depth profiling, these limitations are largely overcome when we make proper synergistic use of IBA methods. In this Tutorial Review we aim to briefly explain to analysts what IBA is and why it is now a general quantitative method of great power. Analysts have got used to the availability of the large synchrotron facilities for certain sorts of difficult problems, but there are many much more easily accessible mid-range IBA facilities also able to address (and often more quantitatively) a wide range of otherwise almost intractable thin film questions.