A membrane supported biofilm reactor uses modules having fine, hollow fibers, for example, made from melt spun thermoplastic polymers treated after spinning to increase their permeability to oxygen, used, for example, in tows or formed into a fabric. In one module, one or more sheets of the fabric are potted into a module to enable oxygen containing gas to be supplied to the lumens of the hollow fibers. Various reactors and processes, for example to treat wastewater, using such modules are described. In one process, oxygen travels through fibers, optionally through an attached biofilm, to oxygenate surrounding water. Mechanical, chemical and biological methods, for example endogenous respiration, are used to control the thickness of the biofilm.