Fiber structures that include a catalytic material are provided. The fiber structures (e.g., membranes) may be formed of interconnected carbon fibers. The catalytic material may be in the form of nanosize particles supported on the fibers. In one method of the invention, the structures are produced by electrospinning a polymeric material fiber structure that is subsequently converted to a carbon fiber structure in a heat treatment step which also causes the catalytic material particles to nucleate on the carbon fibers and grow to a desired size. The catalytic material may be uniformly distributed across the carbon fiber structure and the amount of catalytic material may be controlled. These factors may enhance catalytic performance and/or enable using less catalytic material for equivalent catalytic performance which can lead to cost savings, amongst other advantages. The fiber structures may be used in a variety of applications including electrodes in batteries and fuel cells.