Fiber-reinforced epoxy composites are used in various branches of industry because of their favorable strength and thermal properties, resistance to chemical and atmospheric conditions, as well as low specific gravity. This review discusses the mechanical and thermomechanical properties of hybrid epoxy composites that were reinforced with glass, carbon, and basalt fabric modified with powder filler. The modification of the epoxy matrix mainly leads to an improvement in its adhesion to the layers of reinforcing fibers in the form of laminate fabrics. Some commonly used epoxy matrix modifiers in powder form include carbon nanotubes, graphene, nanoclay, silica, and natural fillers. Fiber fabric reinforcement can be unidirectional, multidirectional, biaxial, or have plain, twill, and satin weave, etc. Commonly used methods of laminating epoxy composites are hand lay-up process, resin transfer molding, vacuum-assisted resin transfer molding, and hot or cold pressing. The following review is a valuable source of information on multiscale epoxy composites due to the multitude of technological and material solutions.