A filter apparatus positionable outside a washing machine and connectable to a drain device of the washing machine, the filter apparatus including a filter case including a case inlet configured so that, with the filter apparatus connected to the drain device, water from the drain device is flowable through the case inlet into the filter case, and a case outlet configured so that, with the filter apparatus connected to the drain device, water in the filter case is flowable through the case outlet out of the filter case; a filter detachably mountable inside the filter case so that water flowing through the case inlet is flowable through a surface of the filter to filter foreign substances from the water, and then to the case outlet; a filter cleaning device configured to clean the surface of the filter; and a controller configured to control the filter cleaning device.