The application of fibre-reinforced polymers (FRP) for strengthening timber structures has proven its efficiency in enhancing load-bearing capacity and, in some cases, the stiffness of structural elements, thus providing cost-effective and competitive alternatives both in new design and retrofitting existing historical buildings. Over the last few decades, several reinforcing materials and techniques evolved, and considerable progress was made in numerical modelling, especially using the finite element method. As this field of research has become extensive and diversified, as well as numerous contradicting results have emerged, a thorough review is necessary. This manuscript covers the topics of historical preliminaries, reinforcing with carbon and glass fibre composites, bond characteristics, main reinforcing techniques, modelling of knots, and the effects of the fibre waviness on the composite behaviour. A detailed overview is given on the experimental and numerical investigation of mechanics of strengthened beams. A one-of-a-kind table is presented that compares the stiffness improvement observed in several studies with analytical estimates. Attention is drawn to a number of challenges that have arisen, e.g., the moderate stiffness enhancement, composite-to-wood interface, modelling of knots, and strengthening of defected timber members. This paper can be used as a starting point for future research and engineering projects.