Fibre-reinforced polymer materials (FRP) are increasingly used to reinforce structural elements. Due to this, it is possible to increase the load-bearing capacity of polymer, wooden, concrete, and metal structures. In this article, the authors collected all the crucial aspects that influence the behaviour of concrete elements reinforced with FRP. The main types of FRP, their characterization, and their impact on the load-carrying capacity of a composite structure are discussed. The most significant aspects, such as type, number of FRP layers including fibre orientation, type of matrix, reinforcement of concrete columns, preparation of a concrete surface, fire-resistance aspects, recommended conditions for the lamination process, FRP laying methods, and design aspects were considered. Attention and special emphasis were focused on the description of the current research results related to various types of concrete reinforced with FRP composites. To understand which aspects should be taken into account when designing concrete reinforcement with composite materials, the main guidelines are presented in tabular form.