Dimensionally stable nonwoven fibrous webs include a multiplicity of continuous fibers formed from one or more thermoplastic polyesters and polypropylene in an amount greater than 0% and no more than 10% by weight of the web. The webs have at least one dimension which decreases by no greater than 10% in the plane of the web when heated to a temperature above a glass transition temperature of the fibers. A spunbond process may be used to produce substantially continuous fibers that exhibit molecular orientation. A meltblown process may be used to produce discontinuous fibers that do not exhibit molecular orientation. In some embodiments, the fibers comprise a viscosity modifier and/or an anionic surfactant. The webs may be used as articles for filtration, sound absorption, thermal insulation, surface cleaning, cellular growth support, drug delivery, personal hygiene, medical apparel, or wound dressing.