Polymer-based composite materials are ideal for applications where high stiffness-to-weight and strength-to-weight ratios are required. From aerospace and aeronautical field to biomedical applications, fiber-reinforced polymers have replaced metals, thus emerging as an interesting alternative. As widely reported, the mechanical behavior of the composite materials involves investigation on micro- and macro-scale, taking into consideration micromechanics, macromechanics and lamination theory. Clinical situations often require repairing connective tissues and the use of composite materials may be suitable for these applications because of the possibility to design tissue substitutes or implants with the required mechanical properties. Accordingly, this review aims at stressing the importance of fiber-reinforced composite materials to make advanced and biomimetic prostheses with tailored mechanical properties, starting from the basic principle design, technologies, and a brief overview of composites applications in several fields. Fiber-reinforced composite materials for artificial tendons, ligaments, and intervertebral discs, as well as for hip stems and mandible models will be reviewed, highlighting the possibility to mimic the mechanical properties of the soft and hard tissues that they replace.