Robotic surface-cleaning assemblies include a base configured to be operatively coupled to a robotic arm; a supply of cleaning fabric supported relative to the base; an applicator supported relative to the base, wherein the applicator is configured to support a portion of cleaning fabric from the supply of cleaning fabric and operatively and selectively position the portion into engagement with a surface to be cleaned; and a source of cleaning fluid supported relative to the base, wherein the source of cleaning fluid is configured to operatively and selectively (i) deliver cleaning fluid directly to the portion of cleaning fabric supported by the applicator and/or (ii) deliver cleaning fluid directly to the surface to be cleaned. Methods of cleaning a surface with a robotic surface-cleaning assembly also are disclosed.