Mops comprising one or more cleaning members. In select embodiments, the cleaning members are releasably secured to the mop and may be capable of compression. In these embodiments, the different cleaning members enable the mop to operate in a plurality of different modes, including a wringing mop mode, a damp mop mode and a dust mop mode. In other embodiments, a portion of the handle of the mop is adapted to hold and release a fluid, such as a cleaning solution. In these embodiments, the user may cause release of the fluid through one or more openings associated with the mop.