There have been great advances in the methods of fragment-based ligand discovery over the past 25 years, with many compounds in the clinic and several fragment-derived drugs now treating patients. The essential feature of the approach is that drug discovery begins with screening of a relatively small library (typically 1000s) of compounds of low molecular weight (average 200 Da). The fragment hits are then evolved, usually guided by the structure of the compounds bound to the therapeutic target, to larger lead compounds which can then be optimised by conventional medicinal chemistry methods. This chapter provides an overview of the current practise of fragment-based ligand discovery. The emphasis is on practical aspects of the methods. Although there are some examples of fragments binding to other targets, the methods have been mostly applied to protein targets, which will be the focus of this discussion. In addition, a section describing some of the history of the evolution of fragment-based discovery is included.