1. Introduction 2. Brittle structures in the field 3. Theoretical aspects 4. Fault slip inversion methods 5. Inversion of tensile fractures 6. Inversion of calcite twins 7. Determining Paleostresses with 'Incomplete' Data 8. One step beyond: full determination of paleostress tensors 9. Examples of applications of stress inversion methods in tectonic analyses 10. A guide to Paleostress Analysis 11. References