A cleaning wipe that includes polyisobutylene (also sometimes referred to as polybutylene or as polybutene). Typically a substantial portion of the polyisobutylene has a molecular weight (MW) greater than 30,000 and in some particular applications the molecular weight is around 85,000. The polyisobutylene is generally disposed at the surface of a porous substrate, such as a non-woven or woven fabric. A method of making a cleaning wipe is provided. The method typically involves dissolving polyisobutylene in a solvent such as hexane to form a tackifier solution, soaking the substrate in the tackifier to produce a preform, and then drying the preform to produce the cleaning wipe. The cleaning wipes are typically used dry, without any liquid cleaning agent. The surface to be cleaned is wiped with a surface of the cleaning wipe at which polyisobutylene is disposed. Vigorous wiping may be used in applications where contamination is difficult to remove.